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Working Paper 8808
FINANCIAL STRUCTURE AND THE ADJUSTMENT OF CAPITAL STOCK
by W i l l i a m P. O s t e r b e r g
W i l l i a m P. O s t e r b e r g i s an economist a t t h e
Federal Reserve Bank o f Cleveland. T h i s paper i s
a r e v i s e d v e r s i o n o f t h e second 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 t h e members o f h i s d i s s e r t a t i o n
committee, Donald Hester, C h r i s F l i n n , and Mark
G e r t l e r , f o r h e l p f u l comments and suggestions.
Paul Bauer, Kim Kowalewski, and James Thomson
p r o v i d e d h e l p f u l comments o n 1a t e r d r a f t s .
Working papers o f t h e Federal Reserve Bank of
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 to
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
o f C l e v e l a n d o r of t h e Board of Governors of t h e
Federal Reserve System.
August 1988
ABSTRACT
I n t h i s paper we analyze t h e i n v e s t m e n t d e c i s i o n when 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 .
We assume t h a t t a x r a t e s f a v o r d e b t o v e r e q u i t y b u t t h a t
the cost o f debt increases w i t h the debt- to- tangible- assets r a t i o .
Since t h e
cost o f debt varies w i t h the debt- to- tangible- assets r a t i o , investment 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 .
E u l e r equations f o r t h e f i r m ' s d e c i s i o n s
are estimated w i t h instrumental v a r i a b l e s u t i l i z i n g data f o r the U.S.
manufacturing s e c t o r f r o m 1954 t o 1980.
F i n a n c i a l s t r u c t u r e does n o t have t h e
expected e f f e c t . The r e s u l t s suggest a c l o s e r examination o f t h e i n f l u e n c e o f
i n f l a t i o n on f i n a n c i a l s t r u c t u r e .
FINANCIAL STRUCTURE AND THE ADJUSTMENT OF CAPITAL STOCK
I. I n t r o d u c t i o n
A growing body o f t h e o r e t i c a l l i t e r a t u r e analyzes l i n k s between the r e a l
and f i n a n c i a l decisions o f f i r m s .
However, e m p i r i c a l i n v e s t i g a t i o n s o f
investment decisions assume t h a t f i r m s ' r e a l and f i n a n c i a l d e c i s i o n s can be
t r e a t e d separately.
I n t h i s e m p i r i c a l l i t e r a t u r e , f i n a n c i a l s t r u c t u r e does
n o t v a r y endogenously.
Thus, s t u d i e s of the impact of tax changes do n o t take
i n t o account the l i k e l y response o f f i n a n c i a l s t r u c t u r e and i t s e f f e c t s on
f i n a n c i a l costs and, hence, on investment.
The r e a l decisions o f f i r m s may i n f l u e n c e t h e i r f i n a n c i a l c o s t s through
numerous channels.
Even i f we take t h e view t h a t r e a l and f i n a n c i a l decisions
may be t r e a t e d separately because t h e debt- to- equity r a t i o i s indeterminate,
r e a l and f i n a n c i a l decisions are l i n k e d i n general e q u i l i b r i u m , since the r a t e
of investment i s a f f e c t e d by the r a t e o f r e t u r n on savings.
L i n k s between r e a l and f i n a n c i a l decisions are more d i r e c t i f f i n a n c i a l
s t r u c t u r e i s determinate.
The debt- to- equity r a t i o i s determinate i f tax
r a t e s f a v o r debt, b u t there are r e a l costs t h a t increase w i t h the
debt- to- equity r a t i o .
Tax r a t e s f a v o r debt l a r g e l y because o f the i n t e r e s t
d e d u c t i b i l i t y o f debt a t the corporate l e v e l and because o f the ( u n t i l
r e c e n t l y ) low r a t e o f personal c a p i t a l - g a i n s t a x a t i o n .
Agency problems o r
increased p r o b a b i l i t y o f c o s t l y bankruptcy imply t h a t there a r e costs t o
i n c r e a s i n g the debt- to- equity r a t i o .
I n t h i s paper, we consider the i n t e r a c t i o n between the f i r m ' s choice o f
c a p i t a l stock (and hence i t s r a t e o f investment) and i t s f i n a n c i a l costs. We
focus on the debt- to- tangible- assets r a t i o r a t h e r than on the debt- to- equity
ratio.
I n o u r model, t h e c o s t of d e b t v a r i e s w i t h t h e d e b t - t o - t a n g i b l e - a s s e t s
r a t i o , and p h y s i c a l c a p i t a l i s t h e o n l y t a n g i b l e a s s e t .
G r e a t e r amounts o f
p h y s i c a l c a p i t a l reduce t h e c o s t o f debt, s i n c e p h y s i c a l c a p i t a l i s u s e f u l as
c o l 1a t e r a l .
We a l s o consider t h e f i r m ' s choices o f o t h e r p r o d u c t i v e f a c t o r s .
As
S h a p i r o (1986) has p o i n t e d o u t , models t h a t consider c a p i t a l as t h e o n l y i n p u t
t h a t i s c o s t l y t o a d j u s t conclude t h a t t h e c a p i t a l s t o c k must be q u i t e c o s t l y
t o a d j u s t , s i n c e i t seems t o respond s l o w l y t o changes i n t h e expected
profitability o f capital.
We c o n s i d e r t h e f i r m ' s choices o f p r o d u c t i o n
employment, hours o f p r o d u c t i o n workers, and nonproduction employment, a l o n g
w i t h i t s choice o f f i n a n c i a l s t r u c t u r e and c a p i t a l s t o c k .
The c o s t s o f
changing these i n p u t s , i n c l u d i n g t h e change i n t h e debt c o s t , h e l p t o
determine t h e response o f t h e c a p i t a l s t o c k t o a change i n t a x r a t e s .
The
e s t i m a t e s o f adjustment c o s t s i n d i c a t e whether t h e debt c o s t i s a s i g n i f i c a n t
determinant o f the path o f the c a p i t a l stock.
11.
Re1a t e d L i t e r a t u r e
The h y p o t h e s i s t h a t t a x r a t e s f a v o r d e b t o v e r e q u i t y a t t h e f i r m l e v e l has
g a i n e d wide acceptance.
'
o f debt f o r corporations.
The advantage i s due t o t h e i n t e r e s t d e d u c t i b i 1 it y
Much r e c e n t work has analyzed t h e f i n a n c i n g c h o i c e
when t h e r e a r e non- debt t a x s h i e l d s t h a t i n c r e a s e t h e p r o b a b i l i t y t h a t t h e
i n t e r e s t t a x s h i e l d s may n o t be f u l l y u t i l i z e d (see, f o r example, Barnea,
Talmor, and Haugen C19871 and Zechner and Swoboda C19861).
Increased
leverage, on t h e o t h e r hand, may i n c r e a s e agency c o s t s a s s o c i a t e d w i t h d e b t o r
may i n c r e a s e t h e p r o b a b i l i t y o f bankruptcy.
Estimates of t h e d i r e c t c o s t s o f
bankruptcy, however, seem t o o low t o e x p l a i n observed f i n a n c i a l s t r u c t u r e s .
Agency c o s t s a s s o c i a t e d w i t h d e b t may a r i s e f o r a v a r i e t y of reasons.
Asset t y p e i s an i m p o r t a n t d e t e r m i n a n t of f i n a n c i a l s t r u c t u r e .
S c o t t (1977)
and Myers and M a j l u f (1984) have i n d i c a t e d t h a t s t o c k h o l d e r s may f i n d i t
advantageous t o i s s u e secured debt.
S c o t t p o i n t s o u t t h a t issuance o f secured
d e b t reduces t h e p r o b a b i l i t y t h a t c e r t a i n c o s t s , such as l e g a l damages, w i l l
be p a i d i n t h e event o f b a n k r u p t c y s i n c e t h e c l a i m s of secured c r e d i t o r s have
priority.
Myers and M a j l u f i n d i c a t e t h a t t h e r e may be c o s t s a s s o c i a t e d w i t h
i s s u i n g s e c u r i t i e s i m p l i c i t l y backed by a s s e t s whose v a l u e i s more e a s i l y
measured by i n s i d e r s than o u t s i d e r s .
For b o t h of these reasons, t h e
a v a i l a b i l i t y o f assets t h a t can serve as c o l l a t e r a l enhances t h e v a l u e o f
equity.
This i s s i m i l a r t o arguments made by Myers (1977) t h a t r e l i a n c e on
" assets i n p l a c e " versus growth o p p o r t u n i t i e s enhances e q u i t y v a l u e s i n c e t h e
v a l u e o f assets i n p l a c e i s l e s s dependent on d i s c r e t i o n a r y investment.'
Many e m p i r i c a l i n v e s t i g a t i o n s o f investment d e c i s i o n s u t i l i z e t h e q t h e o r y
o f investment as t h e i r framework.
E a r l y work by Summers (1980) and Hayashi
(1982) assumed t h a t t h e c a p i t a l s t o c k was t h e o n l y i n p u t t h a t was c o s t l y t o
adjust.
However, Shapiro (1986) and Kokklenberg (1984) c o n s i d e r i n t e r r e l a t e d
f a c t o r demands.
I n these s t u d i e s , r e a l resources a r e absorbed when any
productive i n p u t i s adjusted.
These models i m p l y a much r i c h e r p i c t u r e o f
f i r m s ' response t o changes i n i n t e r e s t r a t e s , t a x r a t e s , o r o t h e r f a c t o r s t h a t
a l t e r the r e t u r n t o c a p i t a l .
111.
The Model
We analyze a p a r t i a l e q u i l i b r i u m model o f investment where t h e f i r m
maximizes t h e expected market v a l u e of i t s e q u i t y .
The market v a l u e o f
e q u i t y i s t h e p r e s e n t d i s c o u n t e d v a l u e o f t h e d i v i d e n d s t o be r e c e i v e d b y t h e
shareholders.
Shareholders d i s c o u n t f u t u r e d i v i d e n d s a t t h e a f t e r - t a x
r e q u i r e d r a t e o f r e t u r n on e q u i t y .
I n Appendix A, we show t h a t t h i s o b j e c t i v e a t t i m e 0 can be w r i t t e n as
max
-S~@*(T)~T
y(t>dt
zoEo = f.;e
where
8*t = ( p
+
pt)/(l -
yt
= (1
-
zYt) DIVt/(l -
p
= the a f t e r- t a x r e a l r a t e o f r e t u r n required by stockholders
pt
= t h e expected r a t e o f i n f l a t i o n i n commodity p r i c e s
TC,
= marginal personal c a p i t a l g a i n s t a x r a t e
T,
=
Tct)
T C ~ )
marginal personal d i v i d e n d t a x r a t e
DIV,= t h e d i v i d e n d
z
= t h e p r i c e o f e q u i t y shares i n terms o f goods
E
= t h e number o f e q u i t y shares
We assume t h a t t h e a f t e r - t a x r e a l r e q u i r e d r a t e o f r e t u r n on e q u i t y p,
the tax rates
the f i r m .
T,
and
T,
t,
and t h e r a t e o f in f 1a t i o n a r e exogenous t o
I n t h e s e c t i o n on e s t i m a t i o n we d i s c u s s e x p e c t a t i o n f o r m a t i o n and
i n f o r m a t i o n a l assumptions.
The f i r m ' s r e a l and f i n a n c i a l d e c i s i o n s a t t h e
s t a r t o f period t w i l l n o t influence 8*t, the a f t e r - t a x r a t e o f r e t u r n
r e q u i r e d by shareholders.
Rather, t h e y i n f l u e n c e y t , t h e d i v i d e n d
a d j u s t e d f o r taxes.
IV.
Financial Structure
We assume t h a t t h e r e i s no a d d i t i o n a l e q u i t y i s s u e and t h a t t h e f i r m
minimizes i t s f i n a n c i a l c o s t s by choosing between d e b t and r e t a i n e d e a r n i n g s .
A t t h e margin, t h e c o s t s o f debt and r e t a i n e d e a r n i n g s w i l l be equal t o t h e
firm.
Tax r a t e s f a v o r debt, b u t t h e d e b t c o s t i n c r e a s e s w i t h t h e r a t i o o f
debt t o t a n g i b l e a s s e t s .
The f i r m ' s f i n a n c i a l and investment d e c i s i o n s t h u s
a f f e c t t h e d e b t c o s t by i n f l u e n c i n g t h e d e b t - t o - t a n g i b l e - a s s e t s r a t i o .
The c o n d i t i o n t h a t t a x r a t e s f a v o r debt o v e r r e t a i n e d earnings can be
w r i t t e n as
where
SO
= b e f o r e - t a x c o s t o f d e b t issued a t t i m e 0.
The c o s t t o s t o c k h o l d e r s o f one d o l l a r o f r e t a i n e d e a r n i n g s a t time 0
i s t h e foregone one d o l l a r o f d i v i d e n d s .
i s the l e f t side o f expression (4).
The p r e s e n t v a l u e o f t h i s c o s t
The c o s t o f one d o l l a r o f debt
i s s u e d a t t i m e 0 i s t h e r e d u c t i o n i n d i v i d e n d s p a i d a t t i m e 1.
The
present value o f t h i s cost i s the r i g h t side o f expression (4), using the
d e f i n i t i o n o f 8* and
SO,
and t a k i n g i n t o account t h e r e d u c t i o n i n t h e
r e a l d e b t burden due t o i n f l a t i o n .
An i n t e r i o r s o l u t i o n f o r t h e f i r m ' s f i n a n c i a l s t r u c t u r e a r i s e s f r o m
t h e combination o f e x p r e s s i o n (4) and t h e assumption t h a t t h e before- tax
c o s t of d e b t i n c r e a s e s w i t h t h e debt- to- tangi ble- assets r a t i o .
The
before- tax c o s t of d e b t i s s u e d i n p e r i o d t i s w r i t t e n as
st = [a + vl(Bt/[(Kt))1Bt
where
t,
Bt
= book v a l u e o f debt i s s u e d a t t h e s t a r t o f p e r i o d
Kt
= n e t s t o c k o f p h y s i c a l c a p i t a l i n p l a c e a t t h e s t a r t o f p e r i o d t, and
E(K,)=
book v a l u e o f K t .
a and v l a r e parameters t o be estimated.
We assume t h a t a l l debt i s
r o l l e d o v e r each p e r i o d and t h a t i n t e r e s t i s p a i d each p e r i o d on t h e e n t i r e
s t o c k o f debt.
C o n d i t i o n (5) i n d i c a t e s t h a t t h e before- tax c o s t o f d e b t
v a r i e s w i t h t h e r a t i o o f t h e book v a l u e o f d e b t t o t h e book v a l u e o f t h e
physical c a p i t a l stock.
[(Kt),
We assume t h a t the book value o f physical c a p i t a l ,
i s a f u n c t i o n o f the n e t stock o f physical c a p i t a l , K t .
[ ( K t > and Kt w i l l d i f f e r f o r a v a r i e t y o f reasons; f o r example, book
d e p r e c i a t i o n i s n o t n e c e s s a r i l y equal t o physical d e p r e c i a t i o n .
we assume t h a t the r a t i o between S ( K t ) and K t , A t
=
S(Kt)lKt,
i s known t o t h e f i r m , although i t v a r i e s through time.
d i r e c t l y and thus chooses [(Kt)
V.
However,
The f i r m chooses Kt
indirectly.
Factor Demands
Following Shapiro (19861, we assume t h a t the production f u n c t i o n i s given
by
log y t
=
a. + a K l o g K t + a L l o g L t + a H l o g H t + a N l o g N t
- . S [ g ~ ~ ( K t + l - d t K , ) ' + ~ L L ( L ~ - q t - i L t - 1 )+'
+
1'
~ H H ( H ~ - H t - 1
gNN(Nt-Nt-,)'l + a , t + c t
where
y t = real output,
K t = physical c a p i t a l stock a t beginning o f p e r i o d t,
Lt = production employment i n p e r i o d t,
H t = weekly hours per production worker i n p e r i o d t,
N t = nonproduction employment i n p e r i o d t,
dt = one minus the physical d e p r e c i a t i o n r a t e o f c a p i t a l ,
q t = one minus the q u i t r a t e , and
e t = shock t o the production f u n c t i o n .
Here the costs o f gross adjustments i n the l e v e l o f the f a c t o r s are
expressed i n terms o f o u t p u t losses.
We have assumed t h a t f a c t o r demands are
not i n t e r r e l a t e d ; the cost o f a d j u s t i n g a s i n g l e i n p u t does n o t depend on
changes i n t h e o t h e r i n p u t s .
The e m p i r i c a l r e s u l t s o f Shapiro and Kokklenberg
have been i n c o n c l u s i v e r e g a r d i n g the s i g n i f i c a n c e o f such i n t e r r e l a t e d n e s s .
The p r o d u c t i v e time l o s t because o f r e o r g a n i z i n g production and i n s t a l l i n g
equipment should vary w i t h n e t investment p l u s depreciation, n o t j u s t w i t h n e t
investment, since e m p i r i c a l l y i t may be d i f f i c u l t t o d i s t i n g u i s h between the
two.
S i m i l a r l y , costs a r e i n c u r r e d i n t r a i n i n g new employees even if the
l e v e l o f p r o d u c t i o n employment i s unchanged.
The cost o f t r a i n i n g new
employees i s d i s t i n c t f r o m the costs o f i n c r e a s i n g hours per employee (such as
overtime).
The c o s t o f p r o d u c t i o n and nonproduction employment i s expressed as
Wt*LtHt + f k L t
+
(7)
f:N,
where
= wage r a t e f o r p r o d u c t i o n workers i n c l u s i v e o f overtime,
Wt*
:
f:
=
f
nonwage c o s t o f a p r o d u c t i o n worker, and
= c o s t o f a nonproduction worker.
w , i s t h e overtime premium.
costs.
f: and f: are nonwage
For nonproduction workers, f: i n c l u d e s s a l a r i e s and f r i nge
b e n e f i t s . For p r o d u c t i o n workers, f: i n c l u d e s o n l y f r i n g e b e n e f i t s .
The
wage b i l l , o r v a r i a b l e c o s t o f p r o d u c t i o n employment, i s w r i t t e n as
W,*LtHt
= WtLtCHt
+
wo
+ wl(Ht-H*t)l
(8)
where
H
T
= l e v e l o f hours a t which overtime s t a r t s ,
Ht-Ht*
= overtime hours per p r o d u c t i o n employee, and
Wt
= wage r a t e f o r p r o d u c t i o n workers e x c l u s i v e o f overtime.
w o and w , are parameters t o be e ~ t i m a t e d . ~w , should be
p o s i t i v e i f the wage b i l l i s t o increase w i t h overtime hours.
This
f o r m u l a t i o n suggests t h a t any "slow" adjustment i n hours may be p a r t i a l l y due
t o an i n c r e a s e i n t h e wage r a t e as o v e r t i m e hours r i s e .
Gross changes i n t h e l e v e l o f investment, K t , a r e f i n a n c e d t h r o u g h d e b t
i s s u e , r e t a i n e d e a r n i n g s , o r t h e decrease i n t h e r e a l debt burden due t o
inflation.
D t I t = REt
T h i s i s expressed i n c o n d i t i o n ( 9 ) .
+ (Bt+1 - Bt) + ptBt
(9)
where 13, i s t h e r e l a t i v e p r i c e o f investment goods.
I n a d d i t i o n , t h e f i r m r e c e i v e s an investment t a x c r e d i t , I T C t , on each
d o l l a r o f investment e x p e n d i t u r e a t t i m e t and i s a b l e t o deduct d e p r e c i a t i o n
expenses i n accordance w i t h t h e t a x code.
Below, Dt equals t h e p r e s e n t
d i s c o u n t e d value o f a l l d e p r e c i a t i o n deductions a s s o c i a t e d w i t h one d o l l a r o f
investment a t time t.
T o t a l revenue i s a t y t , where at i s t h e p r i c e o f o u t p u t a t t i m e
t.
T o t a l revenue e q u a l s t h e sum o f wages, nonwage payments t o l a b o r , taxes,
i n t e r e s t , d i v i d e n d s , and r e t a i n e d e a r n i n g s .
I n appendix A, expressions (6),
(71, (81, and ( 9 ) a r e used t o s o l v e f o r t h e d i v i d e n d .
Using these r e s u l t s , a
d i s c r e t e t i m e v e r s i o n o f e x p r e s s i o n (11, t h e market v a l u e o f e q u i t y a t t i m e 0,
i s w r i t t e n as
Here i n f l a t i o n has complex e f f e c t s on investment, as we would expect g i v e n
p r e v i o u s i n v e s t i g a t i o n s (see F e l d s t e i n [ I 9 8 7 1 and C h i r i n k o C19871).
First,
t h e investment t a x c r e d i t i s based on t h e h i s t o r i c a l c o s t of investment goods,
n o t r e a l expenditures.
Second, d e p r e c i a t i o n deductions a r e a l s o based on
h i s t o r i c a l c o s t r a t h e r than on t h e replacement c o s t .
Third, t h e expression
f o r the dividend includes a term, ptBt, t h a t roughly accounts f o r the f a c t
t h a t i n f l a t i o n erodes the r e a l debt burden.
VI.
Optimal Factor Demands and F i n a n c i a l S t r u c t u r e
A t the beginning o f p e r i o d t
=
0,1,2,3,
...
the f i r m maximizes the expected
value o f V t c o n d i t i o n a l on i n f o r m a t i o n a v a i l a b l e a t the s t a r t o f p e r i o d t
and i n i t i a l c o n d i t i o n s , Kt
Bt = B,.
=
Kt, L t - l = L t - , , N t - l = N t - l ,
Ht-l
= Ht-,,
and
Since B t and Kt a r e given a t the s t a r t o f p e r i o d t, the f i r m chooses
B t + , and K t + , as w e l l as L t , Nt, and H,.
The f o l l o w i n g f i r s t - o r d e r c o n d i t i o n s h o l d f o r a l l t = 0,1,2,
... :
l i m a(Et-,VT) = 0
TaLT
l i m a(Et-,VT)
TaH T
=
0
l i m a(Et-IVT) = 0
TaNT
l i m a(Et-lVT) = 0
a6T
l i m a(Et-IVT) = 0
TaKT
Each E u l e r equation r e q u i r e s t h a t i t i s n o t p o s s i b l e t o increase expected
market value by f u r t h e r increases i n K t , L t , N t , H t , o r B,.
e x p e c t a t i o n terms, marginal b e n e f i t equals marginal c o s t .
In
The choices of
K t , L t , N t , and H, depend d i r e c t l y on t h e e x p e c t a t i o n o f t h e i r values
i n the n e x t p e r i o d , because adjustment c o s t s i n p e r i o d t + l depend on t h e
change between p e r i o d s .
As I demonstrate i n appendix B, expression (14) s t a t e s t h a t t h e expected
c o s t o f funds i s e q u a l i z e d between r e t a i n e d earnings and debt issue.
The
choices o f debt and p h y s i c a l c a p i t a l a r e l i n k e d through t h e i r j o i n t impact on
t h e c o s t o f debt.
An i n c r e a s e i n K t + l i m p l i e s adjustment c o s t s b u t
increases p e r i o d t cash f l o w v i a d e p r e c i a t i o n deductions and investment t a x
credits.
Increases i n K t + l increase p e r i o d t + l o u t p u t , b u t the o v e r a l l
impact o f an increase i n K t + l on p e r i o d t+l cash f l o w a l s o depends on t h e
f u t u r e choice o f K t + 2 . The i n i t i a l c o n d i t i o n s , t h e t r a n s v e r s a l i t y
c o n d i t i o n s , (16) through (20), and the Euler equations, (11) through ( I S ) ,
w i l l i m p l y a unique s o l u t i o n path when combined w i t h the assumptions t h a t 0 <
1/(1+8*) < 1, and t h a t the p r o d u c t i o n f u n c t i o n i s concave and twice
continuously d i f f e r e n t i a b l e i n K, L, N, and H (see Lucas and P r e s c o t t C19711).
Estimation
VII.
We estimate the parameters of t h e production f u n c t i o n and the debt c o s t
f u n c t i o n w i t h o u t s o l v i n g f o r the f i r m ' s d e c i s i o n r u l e s d i r e c t l y .
We u t i l i z e a
v e r s i o n o f Hansen and S i n g l e t o n ' s (1982) Generalized Instrumental V a r i a b l e s
Estimator, which, given o u r assumptions, i s i d e n t i c a l t o o r d i n a r y n o n l i n e a r
three- stage l e a s t squares.
This approach presents b o t h advantages and
disadvantages.
Decision r u l e s can be d e r i v e d i f , i n a d d i t i o n t o the assumptions mentioned
above t h a t guarantee uniqueness, 1 ) p r i c e s and a l l o t h e r v a r i a b l e s exogenous
t o the f i r m f o l l o w covariance s t a t i o n a r y s t o c h a s t i c processes known t o t h e
firm,
2) the r a t e used t o discount the future, 8*, i s constant, and 3) t h e
production function i s quadratic.
I n appendix B, I show how under these
c o n d i t i o n s the Euler equations can be solved t o show t h a t the f i r m ' s d e c i s i o n s
are r e l a t e d t o i t s expectations o f v a r i a b l e s t h a t a r e n o t i n the i n f o r m a t i o n
set.
Although the f i r m makes f o r e c a s t s o f i t s f u t u r e decisions based on i t s
forecasts o f f u t u r e p r i c e s , taxes, etc.,
i t s a c t u a l choices o f f u t u r e i n p u t
l e v e l s w i l l be made a f t e r a d d i t i o n a l i n f o r m a t i o n has been received.
Because our d i s c o u n t r a t e v a r i e s over time, we do n o t u t i l i z e the d e c i s i o n
r u l e technique.
However, d i r e c t l y e s t i m a t i n g the Euler equations e n t a i l s a
loss o f e f f i c i e n c y .
The d e c i s i o n r u l e method u t i l i z e s more i n f o r m a t i o n by
imposing t h e cross- equation r e s t r i c t i o n s between t h e s t o c h a s t i c processes,
I t may
g e n e r a t i n g t h e f o r c i n g v a r i a b l e s and t h e d e c i s i o n r u l e s themselves.
appear t h a t t h e E u l e r e q u a t i o n method a v o i d s t h e need t o s p e c i f y t h e
s t o c h a s t i c processes g e n e r a t i n g t h e f o r c i n g v a r i a b l e s .
However, Garber and
King (1983) n o t e t h a t E u l e r e q u a t i o n e s t i m a t i o n r e q u i r e s i n f o r m a t i o n a l
assumptions s i m i l a r t o those o f c o n v e n t i o n a l simultaneous equations t h e o r y .
Garber and K i n g p o i n t o u t t h a t E u l e r e q u a t i o n methodology does n o t a v o i d
the need t o s p e c i f y t h e d e t a i l s o f t h e g e n e r a l e q u i l i b r i u m i n which economic
agents make t h e i r d e c i s i o n s .
I n t h e i r g e n e r a l e q u i l i b r i u m model,
i d e n t i f i c a t i o n and e s t i m a t i o n d i f f i c u l t i e s a r i s e when t h e e c o n o m e t r i c i a n i s
unable t o observe s h i f t s i n a g e n t s ' o b j e c t i v e s .
I n o u r case, t h e problem may
a r i s e i f t h e r e a r e a c t u a l l y shocks t o preferences b u t n o t p r o d u c t i o n .
Then,
as a r e s u l t o f h a v i n g i n c o r r e c t l y s p e c i f i e d t h e shocks, we may end up
e s t i m a t i n g p r e f e r e n c e parameters r a t h e r t h a n p r o d u c t i o n parameters.
The f o r m o f t h e s t o c h a s t i c E u l e r e q u a t i o n s (11) t h r o u g h (15) tends
n a t u r a l l y t o suggest use o f t h e " g e n e r a l i z e d i n s t r u m e n t a l v a r i a b l e s e s t i m a t o r "
proposed by Hansen and S i n g l e t o n (1982).
Note t h a t i f
Et-lh(Xt,
8)
=
0,
(21
where X t i s t h e m a t r i x o f a l l endogenous and exogenous v a r i a b l e s and
8 is
t h e v e c t o r o f parameters, t h e n t h e p r o d u c t of each such E u l e r e q u a t i o n and
i n s t r u m e n t s i n t h e i n f o r m a t i o n s e t i s a l s o zero:
Et-lh(Xt, g * Z t =
9.
(22
S u b s t i t u t i n g f o r v a r i a b l e s unknown a t t i m e t i n t h e E u l e r e q u a t i o n s y i e l d s
h(Xt, 8 ) * Z t = g t .
Equation (24) suggests why i t i s n a t u r a l t o i n t e r p r e t t h e g t s as
(23)
forecast e r r o r s .
Et-,{h(Xt,e)
-
Et-lCh(Xt,
The e s t i m a t o r o f
8)I)
=
0.
(24)
8 suggested by Hansen and S i n g l e t o n minimizes a weighted
sum o f t h e p r o d u c t s o f t h e i n s t r u m e n t s and h(Xt,g>.
They d e r i v e t h e
w e i g h t i n g m a t r i x t h a t minimizes asymptotic standard e r r o r s even under
conditional heteroscedasticity.
I assume c o n d i t i o n a l h o m o s c e d a s t i c i t y o f t h e
e t s i n s t e a d , and hence u t i l i z e n o n l i n e a r three- stage l e a s t squares.
As i n s t r u m e n t s I u t i l i z e t h e v a r i a b l e s l i s t e d a t t h e t o p o f t a b l e 1 .
These i n c l u d e a l l v a r i a b l e s dated t-1 b u t none dated t .
Since a l l v a r i a b l e s
dated t a r e r e a l i z e d average values o v e r p e r i o d t, t h e y cannot be i n t h e
f i r m ' s information set a t the s t a r t o f period t.
This a p p l i e s even t o t h e t a x
r a t e s , investment t a x c r e d i t , and d e p r e c i a t i o n d e d u c t i o n schedules.
values o f f u t u r e endogenous v a r i a b l e s a r e n o t known a t t i m e t.
Thus, t h e
Their values
w i l l be chosen a t t h e b e g i n n i n g o f t h e n e x t p e r i o d , a f t e r new i n f o r m a t i o n has
been r e c e i v e d b y t h e f i r m .
I f t h e r e a r e s p e c i f i c a t i o n e r r o r s , then t h e e t s
a r e more than f o r e c a s t e r r o r s .
Instruments dated t are n o t v a l i d i f the
s p e c i f i c a t i o n e r r o r component i s s e r i a l l y c o r r e l a t e d .
For t h e system s t u d i e d , 104 o b s e r v a t i o n s and 11 parameters w i l l be
estimated.
I assume t h e e r r o r terms may be c o r r e l a t e d contemporaneously
across equations b u t n o t through time.
The e x p r e s s i o n f o r t h e wage b i l l (8)
i s e s t i m a t e d a l o n g w i t h t h e E u l e r equations, expressions (11) through (15).
Since t h e E u l e r e q u a t i o n f o r debt c o n t a i n s no c u r r e n t endogenous v a r i a b l e s , I
exclude t h a t e q u a t i o n f r o m e s t i m a t i o n .
I n order t o u t i l i z e the appropriate
r o u t i n e i n t h e Time S e r i e s Processor ( V e r s i o n 4.01, I " s o l v e " each E u l e r
e q u a t i o n f o r t h e corresponding f u t u r e endogenous v a r i a b l e .
Thus, t h e
l e f t - s i d e v a r i a b l e s f o r t h e transformed E u l e r equations a r e L t + l , Ht,l,
N,,,,
and K t + * .
Data a r e d e s c r i b e d i n appendix C.
VIII.
Results
The parameter estimates and a l i s t o f t h e instruments are presented i n
t a b l e 1.
The sets o f s t a r t i n g values, a l l o f which l e d t o the same estimates,
are a v a i l a b l e from the author.
Except where otherwise noted, I r e f e r below t o
the r e s u l t s o f o n e - t a i l e d t t e s t s o f the hypothesis t h a t the parameters are
zero, w i t h t h e a l t e r n a t i v e hypothesis t h a t the parameters are p o s i t i v e .
Of
the 11 parameters estimated, f i v e are s i g n i f i c a n t a t the 5 percent l e v e l .
Both parameters i n the wage b i l l f u n c t i o n , expression (81, a r e
significant.
w o i s s i g n i f i c a n t a t the 10 percent l e v e l and w ,
s i g n i f i c a n t a t the 5 percent l e v e l .
.5,
The estimate o f w , , 0.475,
is
i s near
the t y p i c a l overtime premium.
The estimates o f gNN and g K K are both s i g n i f i c a n t a t the 5 percent
level.
N e i t h e r g L L nor gHH, however, i s s i g n i f i c a n t a t the 10 p e r c e n t
level.
This confirms S h a p i r o ' s r e s u l t s t h a t the o n l y s i g n i f i c a n t c o s t s t o
a d j u s t i n g the l e v e l o f p r o d u c t i o n employment and hours are the a d d i t i o n a l
wages o r s a l a r i e s .
O f the o u t p u t e l a s t i c i t i e s , o n l y the e l a s t i c i t y o f o u t p u t
w i t h r e s p e c t t o L, aL, and the e l a s t i c i t y o f o u t p u t w i t h respect t o N, a ~ ,
a r e s i g n i f i c a n t l y d i f f e r e n t from zero.
level.
Both a r e s i g n i f i c a n t a t t h e 5 p e r c e n t
F o l l o w i n g Shapiro, I i n t e r p r e t t h e reasonableness o f t h e estimates by
c a l c u l a t i n g t h e i m p l i e d changes i n q u a r t e r l y f l o w s a t q u a r t e r l y r a t e s i n 1967
d o l l a r s u s i n g the estimated parameters and a r i t h m e t i c averages o f v a r i a b l e s .
,
For example, u s i n g average values of y and L and the estimate of a ~ I
c a l c u l a t e t h a t the increase i n o u t p u t , gross o f adjustment costs, due t o an
e x t r a m i l l i o n p r o d u c t i o n employees i s $1.7 b i l l i o n .
This amounts t o $6,800
per p r o d u c t i o n employee per year.
I t i s u s e f u l t o compare the o u t p u t and costs o f i n c r e a s i n g p r o d u c t i o n
l a b o r i n p u t v i a increases i n L versus increases i n H.
F i r s t , note t h a t a
one-mi 11i o n i n c r e a s e i n p r o d u c t i o n employment increases q u a r t e r l y hours by
524.87 m i l l i o n .
Since t h i s i n c r e a s e o f 524.87 m i l l i o n hours i n c r e a s e s o u t p u t
by $1.7 b i 11i o n , i n c r e a s i n g p r o d u c t i o n employment so as t o i n c r e a s e hours by
one m i l l i o n hours would i n c r e a s e o u t p u t b y $3.25 m i l l i o n .
The i n c r e a s e i n
compensation r e q u i r e d f o r these a d d i t i o n a l employees i s c a l c u l a t e d from t h e
wage b i l l as W ~ E H , + W , + ~ ~ ( H , - H ~ * > I
and f r o m t h e f i x e d c o s t component,
The c o s t o f i n c r e a s i n g t o t a l hours per q u a r t e r by one m i l l i o n t h r o u g h
i n c r e a s e s i n p r o d u c t i o n employment i s $3.82 m i l l i o n .
Increasing quarterly
hours by one m i l l i o n v i a increases i n hours p e r employee r e q u i r e s an i n c r e a s e
of $4.9 m i l l i o n i n compensation. T h i s i s c a l c u l a t e d f r o m t h e e x p r e s s i o n f o r
t h e wage b i l l as WtL,(l+wl).
I g n o r i n g any adjustment c o s t s f o r H o r L, t h e lower compensation c o s t f o r
L compared w i t h H i m p l i e s t h a t i t i s cheaper t o h i r e and l a y off
i n c r e a s e d demand v i a increased hours.
The e s t i m a t e o f
~
N
t h a n t o meet
iNm p l i e s t h a t a
o n e - m i l l i o n change i n nonproduction employment e n t a i l s . $ I 2 b i l l i o n i n
q u a r t e r l y adjustment c o s t s .
The f i x e d c o s t o f one m i l l i o n n o n p r o d u c t i o n
employees i s $7.97 b i l l i o n , w h i l e t h e a d d i t i o n a l o u t p u t a t t r i b u t e d t o these
workers i s $7.16 b i l l i o n .
The average l e v e l o f f: i m p l i e s t h a t each
n o n p r o d u c t i o n employee was p a i d an average o f almost $32,000 p e r y e a r o v e r t h e
sample p e r i o d .
The e s t i m a t e o f g K K i m p l i e s t h a t changing t h e c a p i t a l s t o c k b y $1 b i 11i o n
e n t a i l s adjustment c o s t s o f $1.22 b i l l i o n .
The e s t i m a t e ' o f aK i s n o t
s i g n i f i c a n t a t t h e 10 p e r c e n t l e v e l ; t h e e s t i m a t e o f v 1 i s s i g n i f i c a n t b u t
negative.
S i n c e e x p l a i n i n g t h e p h y s i c a l c a p i t a l c h o i c e i s a p r i m a r y focus i n t h i s
paper, t h e i m p l a u s i b i l i t y o f t h e e s t i m a t e s o f aK and v l i s d i s c o u r a g i n g .
To see i f t h e i n c l u s i o n o f t h e v l t e r m was r e s p o n s i b l e f o r t h e
insignificance o f the estimate o f a ~ I
, excluded t h e v, t e r m and e s t i m a t e d
t h e Euler equation f o r physical c a p i t a l .
The r e s u l t s , g i v e n i n t a b l e 2,
i n d i c a t e t h a t w i t h o u t t h e v l term, t h e e s t i m a t e o f aK remains i m p l a u s i b l e ;
a ~ s h o u l d be s i g n i f i c a n t and p o s i t i v e .
I a l s o c o n s i d e r t h e p o s s i b i l i t y t h a t I have m i s s p e c i f i e d t h e impact of
i n f l a t i o n on investment.
As i n d i c a t e d p r e v i o u s l y , i n f l a t i o n a f f e c t s
i n v e s t m e n t t h r o u g h i t s impact on d e p r e c i a t i o n deductions, on investment t a x
c r e d i t s , on t h e r e a l d e b t burden f a c i n g t h e f i r m , and on t h e c o s t o f d e b t .
The s e r i e s f o r ITC and D a r e based on a c t u a l d e d u c t i o n s and c r e d i t s and a r e
i n f l u e n c e d by i n f l a t i o n .
I have n o t , however, modeled t h e i m p a c t o f i n f l a t i o n
on t h e c o s t o f d e b t i n e x p r e s s i o n (5).
Since i n f l a t i o n r a t e s seemed t o s h i f t i n t h e l a t e 1960s, one crude way t o
c o n t r o l t h e e f f e c t o f i n f l a t i o n i s by s p l i t t i n g t h e sample p e r i o d .
Table 2
presents the r e s u l t s o f the estimation o f the Euler equation f o r physical
c a p i t a l w i t h t h e sample p e r i o d s p l i t a t t h e end o f t h e second q u a r t e r o f 1968.
The s i g n o f t h e e s t i m a t e of v l i s p o s i t i v e i n b o t h subperiods and i s
s i g n i f i c a n t a t t h e 5 p e r c e n t l e v e l i n t h e e a r l i e r subperiod.
i s n e g a t i v e b u t s i g n i f i c a n t i n b o t h subperiods.
The s i g n o f aK
I n a d d i t i o n , Chow t e s t s
i n d i c a t e r e j e c t i o n o f the hypothesis t h a t the c o e f f i c i e n t s are constant across
t h e t w o subperiods.
T h i s r e s u l t o b t a i i i s whether o r n o t t h e v , term i s
excluded.
IX.
Conclusions
T h i s paper has p r e s e n t e d a p a r t i a l e q u i l i b r i u m model o f a r e p r e s e n t a t i v e
f i r m maximizing t h e expected v a l u e o f i t s e q u i t y v i a i t s c h o i c e of p r o d u c t i o n
l a b o r , nonproduction l a b o r , hours o f p r o d u c t i o n l a b o r , c a p i t a l s t o c k , and d e b t
issue.
I t d i f f e r s from o t h e r e f f o r t s by i t s more complete treatment o f t h e
choice o f f i n a n c i a l s t r u c t u r e .
The f i n a n c i n g choice a f f e c t s t h e p a t h o f t h e
c a p i t a l stock i n the t h e o r y presented.
The Euler equations, t o g e t h e r w i t h an
equation i n d i c a t i n g how t h e average wage r a t e v a r i e s w i t h overtime hours, a r e
estimated w i t h i n s t r u m e n t a l v a r i a b l e s .
Of e m p i r i c a l s t u d i e s of adjustment costs, t h i s study i s c l o s e s t t o t h a t o f
Shapiro.'
Shapiro, however, assumes t h a t overtime s t a r t s a t 40 hours w h i l e
I assume t h a t overtime s t a r t s a t a l e v e l t h a t v a r i e s i n each p e r i o d .
This
d i f f e r e n c e i n s p e c i f i c a t i o n may e x p l a i n why S h a p i r o ' s estimate o f aH i s
s i g n i f i c a n t w h i l e mine i s 'not.
Shapiro a l s o f i n d s aK t o be s i g n i f i c a n t ,
p o s s i b l y because he uses t h e Treasury b i l l r a t e p l u s 3 percent as 8*, w h i l e
I c o n s t r u c t 8* t o i n c o r p o r a t e t a x r a t e s and i n f l a t i o n .
The i n s i g n i f i c a n c e o f aK and t h e "wrong" s i g n f o r v l suggest t h a t t h e
t h e model i n t h i s paper i s misspecified.
A crude attempt t o c o n t r o l f o r t h e
e f f e c t o f i n f l a t i o n on t h e estimates o f a ~ and v l suggests t h a t
m i s s p e c i f i c a t i o n may i n v o l v e t h e measurement o f t h e impact o f i n f l a t i o n on
investment. The s i g n o f a ~ however,
,
remains i m p l a u s i b l e f o r each subperiod;
an i n c r e a s e i n t h e s t o c k o f p h y s i c a l c a p i t a l should increase o u t p u t .
Further
work w i l l be aimed a t i s o l a t i n g t h e f a c t o r s r e s p o n s i b l e for these r e s u l t s .
t e n t a t i v e conclusion may be t h a t t h e r e s u l t s o f o t h e r s t u d i e s need t o be
q u a l i f i e d by t h e i r assumptions about tfie e f f e c t o f f i n a n c i a l s t r u c t u r e on
investment decisions.
A
-1 8-
Glossary o f Terms
8*
= t h e " d i s c o u n t r a t e " a p p l i c a b l e t o q u a r t e r t cash f l o w
p
= f i x e d r e a l r a t e o f r e t u r n r e q u i r e d by s t o c k h o l d e r s
p,
= r a t e o f commodity p r i c e i n f l a t i o n
r,,
=
m a r g i n a l personal r a t e o f c a p i t a l g a i n s t a x a t i o n
T,
=
m a r g i n a l personal r a t e o f d i v i d e n d income t a x a t i o n
T,,
=
corporate p r o f i t s tax r a t e
DIV,
= the dividend
yt
= cash f l o w
y,
= r e a l output o f manufacturing
Kt
= p h y s i c a l c a p i t a l s t o c k a t t h e s t a r t of p e r i o d t
L,
= l e v e l o f p r o d u c t i o n employment i n p e r i o d
H,
=
Nt
= l e v e l o f n o n p r o d u c t i o n employment
d
= one minus t h e q u a r t e r l y r a t e o f p h y s i c a l d e p r e c i a t i o n o f t h e p h y s i c a l
t
weekly hours p e r p r o d u c t i o n worker
capi t a l stock
qt
= one minus t h e q u i t r a t e
S(Kt3= book v a l u e o f t h e s t o c k o f p h y s i c a l c a p i t a l
B,
= book v a l u e o f d e b t
H*,
= l e v e l o f weekly hours p e r employee a t which o v e r t i m e s t a r t s
W*,
= h o u r l y wage r a t e i n c l u s i v e o f o v e r t i m e payments
Wt
= hourlywage r a t e e x c l u s i v e o f overtime
f:
=
f:
= t h e f i x e d c o s t o f a n o n p r o d u c t i o n worker
at
= m a n u f a c t u r i n g o u t p u t p r i c e index
t h e f i x e d c o s t o f a p r o d u c t i o n worker
Bt
=
ct
= shock t o t h e p r o d u c t i o n f u n c t i o n
Dt
= present value
investment goods p r i c e index
o f d e p r e c i a t i o n deductions
ITCt = investment t a x c r e d i t
Table 1
The I n s t r u m e n t s
~
~
t
-
1~ ,p t - 1 ,
Ht-1, Nt-1,
9*t-I,
fk-1,
~ c t - 1 ,
qt-1,
K t , Bt,S(Kt),
time(trend1, l(constant),
Wt-l,
(Ht-1-H
*
t-I),
Dt-I,
ITCt-1, Bt-1,
yt-l,
f!-l.
Estimates o f Parameters i n t h e E u l e r Equations and t h e Wage B i l l
(expressions C111, C121, C131, C151, and C81)
i n t e r c e p t i n wage b i l l f u n c t i o n
o v e r t i m e premium
p r o d u c t i o n worker e l a s t i c i t y
p r o d u c t i o n hours e l a s t i c i t y
n o n p r o d u c t i o n worker e l a s t i c i t y
physical capital e l a s t i c i t y
p r o d u c t i o n l a b o r adjustment c o s t
hours adjustment c o s t
n o n p r o d u c t i o n worker adjustment c o s t
c a p i t a l adjustment c o s t
marginal cost o f borrowing w i t h
r e s p e c t t o book d e b t l b o o k c a p i t a l
NOTE:
Asymptotic t - s t a t i s t i c s a r e i n parentheses.
Number o f o b s e r v a t i o n s : 104.
Table 2
Estimates of Parameters in the Euler Equation for Physical Capital,
Expression (15)
Period:
1954:IIIQ-1968:IIQ
1968:IIIQ-198O:IIQ
Estimates Including v l
Parameter
SSR
7.328
6.813
NOBS
56
48
Parameter
1954:IIIQ-198O:IIQ
Estimates Excluding v l
aK
SSR
NOBS
NOTE: Asymptotic t-statistics are in parentheses.
SSR: Sum of squared residuals.
NOBS: Number of observations.
22.261
104
Footnotes
1.
Haugen and Senbet (1986) p r o v i d e a u s e f u l r e v i e w o f t h i s l i t e r a t u r e .
2. The t h e o r e t i c a l importance o f c o l l a t e r a l i n a general e q u i l i b r i u m model
has been i n v e s t i g a t e d by Bernanke and G e r t l e r (1986). I n t h e i r model, t h e
agency c o s t o f investment i s lower w i t h g r e a t e r c o l l a t e r a l .
3. I assume t h a t a l l workers work H,*
use, H, - H,* i s always p o s i t i v e .
s t r a i g h t - t i m e hours. With t h e d a t a I
4. w, i s i n c l u d e d t o p e r m i t a more general s p e c i f i c a t i o n of t h e response
o f o v e r t i m e wages t o an i n c r e a s e i n hours.
5. S h a p i r o ' s study d i f f e r s f r o m t h a t mine i n t h a t he
1) imposes ar + a L + aN = 1,
2 ) uses a d i f f e r e n t l i s t o f instruments,
3) uses a d i f f e r e n t measure o f t h e c o s t o f c a p i t a l ,
4) assumes t h a t m a x i m i z a t i o n o f t h e market v a l u e o f d e b t p l u s e q u i t y i s t h e
o b j e c t i v e o f t h e f i r m , i m p l y i n g t h a t T, and T, do n o t e n t e r t h e
problem, and
5) s p e c i f i e s t h e wage b i l l f u n c t i o n d i f f e r e n t l y . \
Appendi x A
Here we d e r i v e expression (1) i n the t e x t .
This d e r i v a t i o n f o l l o w s
Summers ( 1 980).
The r e t u r n on the e q u i t y o f t h e f i r m has two components.
a f t e r - t a x c a p i t a l gains
-
1
.
(1--r,)V.
One i s
The o t h e r i s a f t e r - t a x dividends
1The t o t a l must equal t h e r e t u r n r e q u i r e d by stockholders
p, a d j u s t e d f o r the r a t e o f i n f l a t i o n .
This i m p l i e s
To prevent the s o l u t i o n t o ( A l l from exploding, we assume
(A21
-S~C(~+~,)I(I-T,,)I~U
l i m V, e
= 0.
Then, the value o f the f i r m ' s e q u i t y a t time t can be w r i t t e n as
(A3)
-S:C(~+~,)/(~-T,,>I~U
Vt = SY C(l-~,,)lD1V,e
ds.
(I-Tcs)
Second, we d e r i v e the expression f o r dividends, embedded i n expression
(101, i n the t e x t .
F i r s t , note t h a t revenues equal the sum o f wages, nonwage
payments t o labor, taxes, i n t e r e s t , dividends, and r e t a i n e d earnings.
Next, as i n d i c a t e d i n expression ( 9 ) i n the t e x t , a l l investment i s
financed through r e t a i n e d earnings, new debt issue, o r the d e c l i n e i n the r e a l
burden of debt due t o i n f l a t i o n .
The term ptBt i s t h e revenue accruing t o
the f i r m because the bonds a r e assumed t o be denominated i n nominal terms.
S u b s t i t u t i n g f o r RE i n (A41 and s o l v i n g f o r RE y i e l d s expression (10).
Expression ( A 3 ) i m p l i e s t h a t t h e c a p i t a l gains t a x r a t e i n f l u e n c e s the value
o f the f i r m o n l y if the value o f the f i r m i s expected t o change.
suppose a l l terms e n t e r i n g i n t o V o are constant.
f o l 1ows :
For example,
Then ( A l l can be solved as
However, suppose t h a t a t t i m e T > 0 d i v i d e n d s increased.
Then t h e v a l u e
o f the f i r m a t t i m e T w i l l r i s e , i m p l y i n g c a p i t a l g a i n s between t i m e 0
and time T.
In t h i s case, t h e v a l u e o f t h e firm a t t i m e 0 can be w r i t t e n
T h i s i m p l i e s t h a t a [ < a V o / a D i v > l < 0.
a~,
Appendix B
The f i r s t - o r d e r c o n d i t i o n f o r production employment (111, can be solved
subject 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 (16) and t h e i n i t i a l c o n d i t i o n t o
y i e l d a d e c i s i o n r u l e f o r production employment.
Assuming a l l terms i n
expression ( 1 1 ) o t h e r than L t + l are i n the i n f o r m a t i o n s e t a t t h e s t a r t of
p e r i o d t, I can r e p l a c e expression (11) w i t h t h e f o l l o w i n g expression:
This can be r e w r i t t e n as
where G i s the l a g operator.
I have assumed t h a t Al,
information s e t a t the s t a r t o f p e r i o d t.
f o l 1ows :
Al,
and A,,
and A2, are i n the
are d e f i n e d as
Expression (B2) can be r e w r i t t e n as
I n o r d e r t o s a t i s f y t h e t r a n s v e r s a l i t y c o n d i t i o n (161, I must s o l v e e i t h e r
forward o r backward, depending on t h e magnitude of A Z t / A l t .
assume t h a t
Azt/Alt
Below, I
< 1.
E s t i m a t i o n o f e x p r e s s i o n (86) r a t h e r t h a n t h e E u l e r e q u a t i o n (11) would
be complicated by a v a r i e t y of f a c t o r s .
F i r s t , since A Z t / A l
may v a r y
through time, i t i s p o s s i b l e t h a t f o r a g i v e n t, f o r example t o , (85) would
have t o be s o l v e d f o r w a r d w h i l e f o r another t, t l , (B5) would have t o be
s o l v e d backward.
Second, e s t i m a t i o n of e x p r e s s i o n (85) would r e q u i r e a
s p e c i f i c a t i o n o f t h e f o r m o f t h e e x p e c t a t i o n s a p p e a r i n g on t h e r i g h t s i d e .
Appendix C
A l l o f t h e d a t a employed are seasonally adjusted, q u a r t e r l y data
measured a t q u a r t e r l y r a t e s and p e r t a i n i n g t o a l l manufacturing, except
where noted.
Kt i s t h e stock o f p h y s i c a l c a p i t a l ( b i l l i o n s o f 1967 d o l l a r s ) a t
the s t a r t o f p e r i o d t.
I t i s c a l c u l a t e d by t h e perpetual i n v e n t o r y
met hod:
Kt = Kt-1
-
dKt-1 + It-l/IMPDEF,-1.
d i s a f i x e d (d, = d f o r a l l t ) r a t e o f p h y s i c a l d e t e r i o r a t i o n f o r
s t r u c t u r e s and equipment i n a l l manufacturing estimated by Jorgenson and
Stephenson (1967).
Iti s investment on new p l a n t and equipment i n
manufacturing p u b l i s h e d by t h e Bureau o f Economic Analysis (BEA), and
IMPDEF i s t h e investment p r i c e d e f l a t o r f o r f i x e d n o n r e s i d e n t i a l
investment expenditures published by BEA i n t h e Survey of Current
Business (SCB).
1967 p r i c e s .
The n e t a d d i t i o n s t o t h e c a p i t a l s t o c k are expressed i n
The s t a r t i n g value f o r K, K I q s 4 : 1 0 , i s t h e v e t stock of
s t r u c t u r e s and equipment i n manufacturing a t the end o f 1953 i n 1967
p r i c e s as p u b l i s h e d i n SCB.
L t i s t h e average number o f p r o d u c t i o n workers ( i n m i l l i o n s )
employed i n a given q u a r t e r .
I t i s o b t a i n e d by averaging t h e monthly
data p u b l i s h e d by t h e Bureau o f Labor S t a t i s t i c s i n Employment and
Earnings ( E E ) .
I n o r d e r t h a t a l l terms i n t h e Euler equations and the
expression f o r t h e cash f l o w be i n b i l l i o n s o f d o l l a r s , I m u l t i p l y L by
.001.
N, i s t h e average number o f nonproduction employees ( i n m i l l i o n s )
over t h e q u a r t e r .
The m o n t h l y number i s c a l c u l a t e d as t h e d i f f e r e n c e
between t o t a l employment and p r o d u c t i o n worker employment f o r t h e
manufacturing sector.
The q u a r t e r l y l e v e l i s t h e average o f t h e l e v e l s
f o r t h e t h r e e months i n t h e q u a r t e r .
The source i s EE.
As f o r L, N must
be m u l t i p l i e d by .001 i n t h e E u l e r e q u a t i o n s .
q, i s t h e q u i t r a t e f o r employment.
monthly, s e a s o n a l l y u n a d j u s t e d b a s i s .
I t i s p u b l i s h e d i n EE on a
I seasonally a d j u s t the a r i t h m e t i c
average o f t h e three- month d a t a i n each q u a r t e r u s i n g an
X-11
seasonal
adjustment procedure.
H, i s t h e average number of hours p e r week f o r p r o d u c t i o n
employment.
I use t h e average o f weekly hours o v e r t h e q u a r t e r .
which i n c l u d e s o v e r t i m e hours, i s p u b l i s h e d i n EE.
H,
I n order t h a t a l l
terms i n t h e E u l e r e q u a t i o n s and t h e e x p r e s s i o n f o r cash f l o w be a t
q u a r t e r l y r a t e s , I m u l t i p l y H by t h e average number o f weeks i n a q u a r t e r .
H, - H*, i s t h e number o f o v e r t i m e hours p e r p r o d u c t i o n employee
per week.
T h i s s e r i e s i s a v a i l a b l e i n EE.
As f o r H, t h i s s e r i e s i s
s c a l e d up by t h e average number o f weeks p e r q u a r t e r .
W , i s t h e average h o u r l y wage r a t e f o r p r o d u c t i o n workers.
This
i s c a l c u l a t e d as t h e average o f t h e m o n t h l y d a t a o v e r t h e q u a r t e r .
b
monthly d a t a a r e p u b l i s h e d i n EE.
W*,
The
W t excludes o v e r t i m e payments.
i s t h e average h o u r l y wage r a t e f o r p r o d u c t i o n workers
i n c l u d i n g overtime.
t h e m o n t h l y averages.
The q u a r t e r l y average i s c a l c u l a t e d as an average o f
The d a t a a r e p u b l i s h e d i n EE. Since these d a t a a r e
a v a i l a b l e o n l y f r o m 1956 onward, I e x t r a p o l a t e back t o 1954 by 1 )
r e g r e s s i n g t h e a v a i l a b l e d a t a on a c o n s t a n t and a t r e n d , 2 ) u s i n g t h e
e s t i m a t e d t r e n d c o e f f i c i e n t t o e x t r a p o l a t e backwards f r o m t h e e s t i m a t e d
intercept.
Since t h i s s e r i e s i s a v a i l a b l e o n l y on an unadjusted b a s i s ,
t h e e n t i r e s e r i e s from 1954 onward was seasonally adjusted u s i n g an X-11
procedure.
f: i s the f i x e d payment per p r o d u c t i o n employee ( b i l l i o n s of
d o l l a r s per m i l l i o n employees).
This i s c a l c u l a t e d from q u a r t e r l y
N a t i o n a l Income and Product Account data.
I c a l c u l a t e the t o t a l f i x e d
c o s t t o t h e sum o f p r o d u c t i o n and nonproduction employees as t h e
difference between t o t a l compensation and the sum o f wages and s a l a r i e s
and employer c o n t r i b u t i o n s t o s o c i a l insurance.
This t o t a l i s then
d i v i d e d by t o t a l employment t o y i e l d f,.
f: i s t h e f i x e d c o s t per nonproduction employee ( b i l l i o n s o f
d o l l a r s per m i l l i o n employees). This i s c a l c u l a t e d as f: p l u s a
s a l a r y component.
The s a l a r y component i s c a l c u l a t e d as wages and
s a l a r i e s minus wages p a i d t o p r o d u c t i o n employees, then d i v i d e d by the
average l e v e l o f nonproduction employment.
The wage b i l l f o r p r o d u c t i o n
employment i s the product o f average h o u r l y wages, t h e number o f
p r o d u c t i o n employees, and t h e average hours per p r o d u c t i o n employee per
quarter.
p i s the r e a l r a t e o f r e t u r n r e q u i r e d by stockholders o v e r a
quarter.
This i s c a l c u l a t e d from d a t a on common stock r e t u r n s p u b l i s h e d
by I b b o t s o n and Sinquefeld (1982).
I t i s the d i f f e r e n c e between t h e
q u a r t e r l y t o t a l r a t e o f r e t u r n on common stocks and the q u a r t e r l y r a t e of
change i n the consumer p r i c e index.
is
KT
where ( 1 +
KT)
27x4
The q u a r t e r l y t o t a l r a t e o f r e t u r n
= the r a t i o between t h e end-of-1980
i n d e x on t o t a l r e t u r n s on common stock and the end-of-1953 index on t o t a l
returns.
The q u a r t e r l y r a t e o f change i n t h e consumer p r i c e index i s
c a l c u l a t e d as
KP
where ( 1
+
K P ) ~ ' "=
~
t h e r a t i o between t h e end
of 1980 consumer p r i c e index and t h e end o f 1953 consumer p r i c e index.
Thus, p i s a q u a r t e r l y r a t e o f r e t u r n constant from 1954 t o 1980.
p
i s c a l c u l a t e d from seasonally unadjusted data.
p t i s t h e r a t e o f change i n t h e consumer p r i c e index f o r urban
workers over p e r i o d t.
This i s a v a i l a b l e i n SCB.
i s t h e marginal personal d i v i d e n d income t a x r a t e .
T,
This
s e r i e s i s c a l c u l a t e d by E s t r e l l a and Fuhrer (1983) from annual i n d i v i d u a l
income t a x r e t u r n s .
Thus,
T~
i s a v a i l a b l e o n l y on an annual b a s i s .
I assume t h a t t h e r a t e f o r each q u a r t e r i s equal t o t h e r a t e f o r t h e
e n t i r e year.
T,
i s t h e personal c a p i t a l gains t a x r a t e .
I f o l l o w Summers'
(1980) and B a i l e y ' s (1969) treatment o f the e f f e c t o f d e f e r r a l and t h e
l a c k o f c o n s t r u c t i v e r e a l i z a t i o n a t death on the e f f e c t i v e t a x r a t e .
B a i l e y concludes t h a t from 1932 t o 1969, each o f these f a c t o r s halved t h e
effective rate.
Since over t h i s p e r i o d the s t a t u t o r y t a x r a t e on c a p i t a l
gains was h a l f t h a t on dividends, I use 12.5 percent o f t h e d i v i d e n d t a x
r a t e from E s t r e l l a and Fuhrer as
T,
f o r 1954 t o 1969.
I follow
Summers and c i t e the e s t i m a t e o f t h e NBER TAXSIM model t h a t t h e 1969
c a p i t a l gains r e f o r m made t h e r a t e 50 percent h i g h e r o r 18.75 percent o f
the dividend rate.
T,
i s the corporate p r o f i t s tax rate.
I use t h e s t a t u t o r y
c o r p o r a t e p r o f i t t a x r a t e as p u b l i s h e d i n Pechman (1983).
I assume t h a t
q u a r t e r l y r a t e s a r e equal t o t h e annual r a t e .
y t i s t h e o u t p u t o f t h e manufacturing s e c t o r ( b i l l i o n s o f
do1 l a r s ) .
I use t h e Federal Reserve Board's index o f manufacturing
p r o d u c t i o n and i n f l a t e t h e p r o d u c t o f y and a so t h a t t h e average o f
a and y f o r 1967 equals a c t u a l 1967 manufacturing o u t p u t .
1967
manufacturing o u t p u t i s c a l c u l a t e d as equal t o 1967 value o f shipments
p l u s the change i n manufacturing i n v e n t o r i e s over 1967.
Both the
shipments and i n v e n t o r y d a t a a r e published by BEA i n Business
Statistics.
Both a r e unadjusted f o r seasonal v a r i a t i o n .
d a t a i s on a book value b a s i s .
procedure.
The i n v e n t o r y
I seasonally a d j u s t y u s i n g an X-11
The p r o d u c t i o n index i s published monthly, and I use the
average l e v e l o f the index over the q u a r t e r .
a
i s the p r i c e o f manufacturers' goods.
I use the Producer P r i c e
Index f o r manufacturing p u b l i s h e d i n Business S t a t i s t i c s .
This index i s
published on a monthly basis, and I use the average index l e v e l f o r the
quarter.
Since t h i s index i s a v a i l a b l e o n l y on an unadjusted basis, I
a d j u s t the q u a r t e r l y data u s i n g an X-11 procedure.
B i s the p r i c e o f investment goods.
I use t h e i m p l i c i t p r i c e
d e f l a t o r f o r f i x e d investment f o r the n o n r e s i d e n t i a l s e c t o r .
R i s based
so t h a t the product o f R and I i s measured i n 1967 d o l l a r s .
I i s investment i n p l a n t and equipment.
As i n d i c a t e d above, I use
BEA's measure o f investment expenditure on p l a n t and equipment.
ITCt i s the investment t a x c r e d i t a t time t from one d o l l a r o f
investment expenditure a t time t. I use the s e r i e s c a l c u l a t e d by
Jorgenson and S u l l i v a n (1981) f o r the e n t i r e corporate s e c t o r .
Their
s e r i e s takes account o f t h e d i s t r i b u t i o n o f investment between s t r u c t u r e s
and equipment as w e l l as the d i s t i n c t i o n between usable and unusable t a x
credits.
This s e r i e s i s thus an " e f f e c t i v e " t a x c r e d i t r a t e .
It i s
published on an annual b a s i s , and I assume the q u a r t e r l y r a t e s are equal
t o the annual r a t e .
D t i s the present value a t time t o f a l l c u r r e n t and f u t u r e
d e p r e c i a t i o n deductions from one d o l l a r o f investment a t time t.
Jorgenson and S u l l i v a n p u b l i s h t h i s s e r i e s on an annual basis.
I assume
t h a t t h e q u a r t e r l y r a t e s equal t h e annual r a t e .
Jorgenson and S u l l i v a n
calculate t h e i r series from a simulation o f the corporate sector taking
account o f t h e d i s t r i b u t i o n o f investment across i n v e s t m e n t types.
They
a l s o t a k e i n t o account evidence r e g a r d i n g a c c o u n t i n g p r a c t i c e s , c a p i t a l
l i f e t i m e s , and salvage values.
((Kt)
dollars).
i s t h e book v a l u e o f c a p i t a l a t t i m e t ( b i l l i o n s o f
I use t h e s e r i e s on t h e book v a l u e o f " d e p r e c i a b l e and
amortizable f i x e d assets, i n c l u d i n g construction i n progress" published
i n t h e Q u a r t e r l y F i n a n c i a l Report (QFR) by t h e Bureau o f t h e Census.
d a t a were s u p p l i e d b y Data Resources I n c .
The
Below I d i s c u s s how I
compensated f o r s e v e r a l d i s c o n t i n u i t i e s w i t h i n t h e s e r i e s .
After this
adjustment, I s e a s o n a l l y a d j u s t t h e data.
B, i s t h e book v a l u e o f debt ( b i l l i o n s o f d o l l a r s ) . I use t h e
s e r i e s on s h o r t term d e b t ( " o r i g i n a l m a t u r i t y o f 1 y e a r o r l e s s " ) ,
" i n s t a l l m e n t s due i n one year o r l e s s on l o n g t e r m d e b t " and " l o n g t e r m
d e b t " (due i n more t h a n one y e a r ) p u b l i s h e d i n t h e QFR.
I adjust f o r
d i s c o n t i n u i t i e s i n these s e r i e s and t h e n s e a s o n a l l y a d j u s t t h e t o t a l o f
these s e r i e s .
Thus, B, excludes " t r a d e accounts" and " d e f e r r e d t a x e s "
and o t h e r l i a b i l i t i e s .
The QFR s e r i e s on t h e book v a l u e o f d e b t and t h e book v a l u e o f t h e
c a p i t a l s t o c k c o n t a i n e d two breaks i n c o n t i n u i t y .
I n 1967 newspapers
were added t o t h e sample and DRI d i d n o t c o n t i n u e t h e s e r i e s f o r w a r d .
In
1974 t h e e n t i r e sampling procedure and q u e s t i o n n a i r e were changed,
causing another break i n t h e s e r i e s .
A v i s u a l examination o f the s e r i e s
suggested t h a t I make a l e v e l adjustment f o r t h e 1973:IVQ t o 1974:IQ
break.
I accomplished t h i s u s i n g t h e o v e r l a p d a t a a v a i l a b l e f o r those
two q u a r t e r s .
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@FedFRASER