INFLATION, INTEREST RATES AND TRANSACTIONS COSTS: THE U.S. EXPERIENCE, 1953-1979
J o h n C h a r l e s A m b r o s e
U N I V E R S I T Y OF L O N D O N
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INFLATION, INTEREST RATES AND TRANSACTIONS COSTS: THE U.S. EXPERIENCE 1953-1979
J o h n C h a r l e s A m b r o s e
A B S T R A C T
This t h e s i s c o n t a i n s t h r e e p r i m a r y a s p e c t s : a n
a n a l y s i s of the a c t u a l i n f l a t i o n - i n t e r e s t r a t e r e l a t i o n s h i p in th e A m e r i c a n e c o n o m y for the 1 9 5 3 - 1 9 7 9 a n d 1 9 5 3 - 1 9 8 3 p e r i o d s in b o t h th e s h o r t - r u n a n d the l on g- ru n, a
d e s c r i p t i o n and a n a l y s i s of the f a i l u r e of o t h e r real
i n t e r e s t rate m o d e l s to a d e q u a t e l y a c c o u n t for the a p p a r e n t f a i l u r e of a "full" F i s h e r e f f e c t to o p e r a t e , a nd e m p i r i c a l t e s t s of a m odel (with some v a r i a t i o n s of it as well) w h i c h sh e d s light o n t h e p h e n o m e n o n of t h e u n d e r a d j u s t m e n t of n o m i n a l rates to i n f l a t i o n e v e n w h e n t h e l o n g e s t of runs is t a k e n into a c c ount. T h e e s s e n t i a l n o t i o n u n d e r l y i n g the m o d e l is that h i g h l y m a r k e t a b l e f i n a n c i a l a s s e t s y i e l d
l i q u i d i t y s e r v i c e s in t h e s e n s e t h a t t h e h o l d i n g of t h e m a l l o w s an ag e n t to r e d u c e his t r a n s a c t i o n s costs of
e x c ha ng e. G i v e n t h a t t h e real r e t u r n o n m o n ey , w h i c h p o s s e s s e s u l t i m a t e l i qu i d i t y , is the n e g a t i v e of the i n f l a t i o n r a t e t h e n it f o l l o w s th a t the r e a l r e t u r n s on a s s e t s w h i c h are r e l a t i v e l y c l o s e to m o n e y in t e r ms of
l i q u i d i t y s e r v i c e s y i e l d e d by t h e m s h o u l d a l s o fall in th e f ac e of i n c r e a s e d i n f l a t i o n . T h e d e g r e e t o w h i c h th e real r e t u r n on any p a r t i c u l a r a s s e t d e c l i n e s is p o s i t i v e l y
r e l a t e d to its ' m o neyness'. Th u s the r e t u r n s on the l o nger term, r e l a t i v e l y i l l i q u i d f i n a n c i a l a s s e t s s h o u l d b e m o r e s u b j e c t to a full F i s h e r e f f e c t t h a n t h o s e on the m o r e m a r k e t a b l e assets.
Th e fi r s t c h a p t e r r e v i e w s some of t h e t h e o r e t i c a l a n d e m p i r i c a l w o r k o n t h e F i s h e r e f f e c t a n d o f f e r s a d e t a i l e d e x p l a n a t i o n of t h e b a s i c mo d e l . An a p p e n d i x d e a l s w i t h a t r a n s a c t i o n s c o s t m o d e l of u n d e r a d j u s t m e n t w h i c h has a m o r e e x p l i c i t role for t r a d i n g c o s t s . C h a p t e r 2 p r e s e n t s t h e e m p i r i c a l e v i d e n c e on u n d e r a d j u s t m e n t in t h e s h o r t a n d long runs a n d c r i t i c a l l y r e v i e w s s o m e w o r k o f o t h e r s a t t e m p t i n g to a c c o u n t for a less t h a n c o m p l e t e F i s h e r e f fect. C h a p t e r 3 d e a l s w i t h d i r e c t t e s t s of t h e m o d e l ' s m o r e i m p o r t a n t i m p l i c a t i o n s c o n c e r n i n g th e d e g r e e of a d j u s t m e n t of n om in a l ra t e s to i n f l a t i o n w i t h r e s p e c t to an a s s e t ' s l i q ui d i t y . In C h a p t e r 4 the h y p o t h e s i s is e n t e r t a i n e d a n d e m p i r i c a l l y
TABLE OF CONTENTS
Chapter Page
L I S T OF T A B L E S ... 5
L I S T O F F I G U R E S ... 6
I N T R O D U C T I O N ... 7
1 G E N E R A L D I S C U S S I O N OF T H E
F I S H E R E F F E C T A N D T HE M O D E L ... 15 I. T h e F i s h e r E f f e c t : D i s c u s s i o n a n d
E m p i r i c a l W o r k ... 15 II. T a x es a n d t he F i s h e r E f f e c t ... 22 III. T h e B a s i c M o d e l a nd the N a t u r e of L i q u i d i t y 27
A P P E N D I X 1
A n A l t e r n a t i v e M o d e l of T r a n s a c t i o n s C o s t s and U n d e r a d j u s t m e n t ... 44
2 T H E F I S H E R E F F E C T IN T H E S H O R T A N D L O N G R U N 52 I. G e n e r a l D i s c u s s i o n and M e t h o d o l o g y ... 52 II. E m p i r i c a l R e s u l t s of th e F i s h e r E q u a t i o n
in t h e S h o r t - R u n ... 57 III. The I n f l u e n c e of K e y V a r i a n c e s on Re a l
R a t e s ... 65 IV. The L o n g - R u n F i s h e r E f f e c t ... 79 V. The F a m a T e s t s on One M o n t h B i l l s ... 88 VI. A C r i t i q u e of the F l a m a S t a g f l a t i o n M o d e l . 103 VII. A C r i t i c a l D i s c u s s i o n of O t h e r R e a l R a t e
M o d e l s a n d C o n c l u s i o n ... 105
A P P E N D I X 1
The I n f l a t i o n - I n t e r e s t R a t e R e l a t i o n s h i p
U n d e r the L u c a s A p p r o a c h ... 115
A P P E N D I X 2
The L e v e l o f I n f l a t i o n a n d Its V a r i a n c e . . 120
A P P E N D I X 3
The C r o s s S p e c t r a l E v i d e n c e o n t h e
I n f l a t i o n - I n t e r e s t R a t e R e l a t i o n s h i p . . . 124
A P P E N D I X 4
The T i m e S e r i e s E v i d e n c e on N o m i n a l R a t e s
and I n f l a t i o n ... 129
A P P E N D I X 5
E x t e n d e d P e r i o d R e s u l t s ... 138
TABLE OF CONTENTS (cont.)
Chapter Page
3 T H E D I F F E R E N T I A L I M P A C T OF I N F L A T I O N ON
V A R I O U S F I N A N C I A L I N S T R U M E N T S ... 144 I. V a r y i n g D e g r e e s of A d j u s t m e n t to I n f l a t i o n
in the F- H M o d e l ... 144 II. T h e I m p a c t of I n f l a t i o n on E q u i t y an d D e b t
Y i e l d s ... 146 III. T e s t s W i t h I n s t r u m e n t s of V a r y i n g
M a r k e t a b i l i t y ... 163 IV. T e s t s w i t h I n s t r u m e n t s of D i f f e r e n t
M a t u r i t y P e r i o d s ... 170
A P P E N D I X 1
S e c t i o n 1. T r a d i n g V o l u m e a n d A b s o l u t e L e v e l s of V a r i o u s M a t u r i t y G o v e r n m e n t
S e c u r i t i e s a n d O t h e r A s s e t s ... 182
S e c t i o n 2. R e s u l t s of C h o w T e s t s for R a n k i n g s of P o i n t I m p a c t of I n f l a t i o n on
V a r i o u s Y i e l d s ... 183
S e c t i o n 3. O r i g i n a t i n g E q u a t i o n s for
R e s u l t s P r e s e n t e d in T a b l e 3 - 4 ... 186
A P P E N D I X 2
M e t h o d U s e d to C o m p u t e H o l d i n g P e r i o d
R e t u r n s ... 191
4 T H E C A P I T A L A S S E T P R I C I N G M O D E L A N D
L I Q U I D I T Y P R E M I A ... 193
I. B a s i c s of the C a p i t a l A s s e t P r i c i n g M o d e l . 194 II. T e s t s of the C A P M ... 196 III. A D i s c u s s i o n of a nd a R e j o i n d e r to R o l l ' s
C r i t i q u e ... 208 IV. E m p i r i c a l R e s u l t s of t h e S h o r t - R u n C A P M
T e s t s ... 211 V. L o w F r e q u e n c y C A P M R e s u l t s ... 224
A P P E N D I X 1
M e t h o d U s e d to C o m p u t e P a r t i a l
C o r r e l a t i o n s ... 232
5 S U M M A R Y A N D C O N C L U S I O N S ... 237
B I B L I O G R A P H Y ... 252
60 63 67 71 76 85 93 95 97 127 133 151 157 168 175 LIST OF TABLES
C H A P T E R 2
S er i al C o r r e l a t i o n S t r u c t u r e of t h e Ex P o s t Real Rate: 1 9 5 3 - 1 9 7 9 ...
T e s t s of the C o n s t a n c y of t h e Re a l R a t e
U t i l i z i n g T im e T r e n d V a r i a b l e s ...
T e s t s of th e C o r r e l a t i o n B e t w e e n R e a l R a t e s and O t h e r V a r i a b l e s ...
T e s t s of the C o r r e l a t i o n B e t w e e n N o m i n a l R a t e s and t h e G o v e r n m e n t s / M o n e y R a t i o ...
P o l y n o m i a l D i s t r i b u t e d L a g M o d e l s of I n f l u e n c e of I n f l a t i o n on I n t e r e s t R a t e s ...
M o v i n g A v e r g a e R e g r e s s i o n s of O n e - M o n t h
T r e a s u r y Bill R a t e s on I n f l a t i o n ...
R e g r e s s i o n s of C h a n g e s i n P u r c h a s i n g P o w e r on N o m i n a l R a t e s ...
A u t o c o r r e l a t i o n s of A t ...
R e g r e s s i o n s of C h a n g e s in P u r c h a s i n g P o w e r on N o m i n a l R a t e s a n d L a g g e d D e p e n d e n t V a r i a b l e V a l u e s ...
C r o s s S p e c t r a l A n a l y s i s of t h e
I n f l a t i o n - I n t e r e s t R a t e R e l a t i o n s h i p 1 9 5 3 - 1 9 7 9
C h i - S q u a r e T e s t s for I n d e p e n d e n c e ...
C H A P T E R 3
R e g r e s s i o n s of Re a l E q u i t y R e t u r n s on
I n f l a t i o n a n d R e a l A c t i v i t y ...
R e g r e s s i o n s of E q u i t y / D e b t Y i e l d S p r e a d on I n f l a t i o n and Real I n c o m e 6 / 1 9 5 3 - 1 2 / 1 9 7 9 . . .
T e s t s of t h e F i s h e r E f f e c t w i t h D i f f e r e n t
E x p e c t a t i o n a l A s s u m p t i o n s a n d I n t e r e s t R a t e s .
T e s t s of U n d e r a d j u s t m e n t (F r i e d - H o w i t t
A n a l y s i s ) ...
LIST OF TABLES (cont.)
Table Page
C H A P T E R 4
4-1 R e s u l t s of the C A P M L i q u i d i t y P r e m i a T e s t s . . 219
4-2 AR(1) R e g r e s s i o n s of C A P M E x c e s s R e t u r n s
( 1 9 7 4 - 1 9 7 9 ) ... 222
4-3 L o n g e r R u n C o r r e l a t i o n C o e f f i c i e n t s of C A P M
T es t V a r i a b l e s ... 227
L I S T OF F I G U R E S
F i g u r e P a g e
C H A P T E R 2
Al-1 L u c a s E x p o n e n t i a l l y - W e i g h t e d C e n t e r e d M o v i n g A v e r a g e T e c h n i q u e W e i g h t = .5
F i l t e r L e n g t h = 2 y e a r s ... 117
Al - 2 L u c a s E x p o n e n t i a l l y - W e i g h t e d C e n t e r e d M o v i n g A v e r a g e T e c h n i q u e W e i g h t = .8
F i l t e r L e n g t h = 2 y e a r s ... 118
A l - 3 L u c a s E x p o n e n t i a l l y - W e i g h t e d C e n t e r e d M o v i n g A v e r a g e T e c h n i q u e W e i g h t = .8
F i l t e r L e n g t h = 4 y e a r s ... 119
A2-1 M e a n a n d S t a n d a r d D e v i a t i o n of I n f l a t i o n
1 9 5 3 - 1 9 7 9 (% pe r Y e a r ) ... 121
A2 - 2 M e a n a n d S t a n d a r d D e v i a t i o n of I n fl at io n,
Q u a r t e r l y P e r c e n t a g e C h a n g e s i n U.S. CPI . . . 121
A4-1 A u t o c o r r e l a t i o n F u n c t i o n ( I n fl at i o n ) ... 136
A 4- 2 A u t o c o r r e l a t i o n F u n c t i o n (One M o n t h M a t u r i t y
Y i e l d s ) ... 136
A 4 - 3 C u m u l a t i v e P e r i o d o g r a m ( I n f l at io n) ... 136
A4 - 4 C u m u l a t i v e P e r i o d o g r a m (One M o n t h M a t u r i t y
Y i e l d s ) ... 137
A 4 - 5 C r o s s C o r r e l a t i o n s ( I n f l a t i o n s a n d One M o n t h
M a t u r i t y Y i e l d s ) ... 137
I N T R O D U C T I O N :
T h i s t h e s i s is e s s e n t i a l l y a c a r e f u l e m p i r i c a l s t u d y of
the i n f l a t i o n - i n t e r e s t r a t e r e l a t i o n s h i p in th e A m e r i c a n
e c o n o m y for t h e 1 9 5 3 - 1 9 7 9 era ( a l t h o u g h t h e s a m p l e p e r i o d is
e x t e n d e d in s o m e s e c t i o n s ) a n d a t e s t of a m o d e l w h i c h
p u r p o r t s to e x p l a i n t h e l e s s - t h a n - f u l 1 a d j u s t m e n t of n o m i n a l
i n t e r e s t r a t e s t o i n f l a t i o n f o u n d in v a r i o u s f i n a n c i a l a s s e t
m a r k e t s o ve r t h i s p e r i o d. T h e m o d e l w a s d e v e l o p e d b y F r i e d
a n d H o w i t t (1983) a n d is b a s e d on t h e f r i c t i o n a s s o c i a t e d
w i t h t r a n s a c t i o n s c o s t s of e x c h a n g e . T h e n o t i o n is t h a t
m a r k e t s i n c o r p o r a t e in v a r i o u s a s s e t r e t u r n s a n a m o u n t w h i c h
r e f l e c t s th e r e l a t i v e d e g r e e of l i q u i d i t y of t he a s s e t in
q u e s t i o n , l i q u i d i t y in t h e s e n s e of t r a n s a c t i o n s c o s t s t ha t
are a v o i d e d b y h o l d i n g t h e asset.
C h a p t e r 1 f o c u s e s on t h e t h e o r e t i c a l f o u n d a t i o n s t h a t
u n d e r l i e m u c h of t h e e m p i r i c a l w o r k on th e i n t e r e s t r a t e
-i n f l a t -i o n r e l a t -i o n s h -i p -in b o t h t he s h o r t a nd l o n g - r u n s an d
c r i t i c a l l y d i s c u s s e s s om e r e c e n t w o r k w h i c h a t t e m p t s to
e x p l a i n w h y r e s e a r c h e r s h a v e f a i l e d to f in d a full F i s h e r
e f fect. F o r e x a m p l e , B l e j e r a n d E d e n (1979) a r g u e t h a t t h e
m e a s u r e d c o e f f i c i e n t o n i n f l a t i o n is d o w n w a r d b i a s e d d ue to
the e x c l u s i o n of a n i n f l a t i o n v a r i a n c e t e r m in an o t h e r w i s e
s t a n d a r d F i s h e r e f f e c t e q u a t i o n . H o w e v e r e v i d e n c e is
p r e s e n t e d t h a t t h i s p a r t i c u l a r a r g u m e n t has l i t t l e r e l e v a n c e
for o u r p e r i o d of i n t e r e s t . It is a l s o d e m o n s t r a t e d in t h e
f i r s t c h a p t e r t h a t th e r e c e n t f o c u s i n g of a t t e n t i o n o n t a x
-a d j u s t e d r e t u r n s b y D -a r b y (1975), F e l d s t e i n (1980 ) et. -a l . ,
h o w e v e r t h e o r e t i c a l l y a p p r o p r i a t e , f a i l s to a c c o u n t for th e
s t y l i z e d f a c t of less t h a n u n i t a d j u s t m e n t . E v e n w h e n
a l l o w i n g fo r m u l t i p l e m a r g i n a l t a x ra t e s , the use of
p l a u s i b l e m a g n i t u d e s for t h e s e v a l u e s i n d i c a t e s t h a t we
s h o u l d f i n d a n o v e r a d j u s t m e n t , a p o i n t t h a t s e e m s t o h a v e
b e e n o v e r l o o k e d b y the w r i t e r s in t h i s area. It is a l s o
a r g u e d t h a t r e a l i n t e r e s t r a t e m o d e l s s u c h as M u n d e l l - T o b i n
fail to a c c o u n t fo r t h e o b s e r v e d f i n d i n g s .
F r i e d a n d H o w i t t (F-H) d e v e l o p e d t h e i r m o d e l w i t h i n t h e
c o n t e x t of b o t h c o n t i n u o u s t i m e a n d t h e lon g - r u n , p a r t l y
b e c a u s e t h e y f e l t t h a t t h e r e w e r e s h o r t - t e r m f a c t o r s t h a t
c o u l d p o t e n t i a l l y e x p l a i n the u n d e r a d j u s t m e n t w i t h i n the
b u s i n e s s c y c l e b u t a l s o b e c a u s e t h e r e w e r e n o g o o d
e x p l a n a t i o n s for th e f a i l u r e of t h e F i s h e r e f f e c t in the
lon g e r r u n (the f a i l u r e of s u p e r n e u t r a l i t y ) o t h e r t h a n o n e
t h a t w o u l d t r e a t a s s e t s as less t h a n p e r f e c t s u b s t i t u t e s for
one a n o t h e r , d i f f e r i n g in the l i q u i d i t y s e r v i c e s t h a t t h e y
p r o v i d e . A n i m p o r t a n t c o n t r i b u t i o n of t h i s t h e s i s is to
d e m o n s t r a t e t h a t the F r i e d - H o w i t t m o d e l p r o v i d e s a s u p e r i o r
i n t e r p r e t a t i o n of th e u n d e r a d j u s t m e n t f i n d i n g s in t h e s h o r t
-run as w e l l as th e l o n g - r u n a n d t h a t s o m e of t h e b e t t e r
k n o w n p o t e n t i a l s h o r t - r u n e x p l a n a t i o n s a r e e i t h e r
m i s c o n c e i v e d or d o n o t s t a n d u p e m p i r i c a l l y , a t l e a s t for
the s a m p l e p e r i o d c o n s i d e r e d in t h e p r e s e n t work. C h a p t e r 1
a l s o i n t r o d u c e s s o m e of the t e r m i n o l o g y u s e d t h r o u g h o u t th e
p r e s e n t s t u d y a n d p r o v i d e s a d i s c u s s i o n of the m o d e l t h a t
h i g h l i g h t s s o m e of its f e a t u r e s w h i c h a r e of t h e g r e a t e s t
c o n t a i n s f u r t h e r c l a r i f i c a t i o n of the F - H a n a l y s i s as w e l l
as a mo d e l w h i c h , u n l i k e F-H, e x p l i c i t l y i l l u s t r a t e s the
ro l e of r e l a t i v e t r a n s a c t i o n s c o s t s in t h e d e t e r m i n a t i o n of
y i e l d d i f f e r e n t i a l s . A d d i t i o n a l l y , t h e ro l e of e x o g e n o u s l y
i s s u e d a s s e t s in h e l p i n g to d e t e r m i n e i n t e r e s t
rate d i f f e r e n t i a l s is m a d e m o r e e x p l i c i t t h a n in F-H.
C h a p t e r 2 is a l m o s t e x c l u s i v e l y d e v o t e d to a n a n a l y s i s
of the a ct ua l i n f l a t i o n - i n t e r e s t r a t e r e l a t i o n s h i p in t h e
U.S. e c o n o m y fo r t he 1 9 5 3 - 1 9 7 9 p e r i o d a l t h o u g h , w h e n
p os si bl e, t he a n a l y s i s is e x t e n d e d t o i n c l u d e t h e e a r l y
1980s, a p e r i o d of a l m o s t u n p r e c e d e n t e d h i g h real i n t e r e s t
rates. On e e m p i r i c a l a p p r o a c h u s e d f o l l o w s t h a t of M i s h k i n
(1981) w h o i n v o k e s a r a t i o n a l e x p e c t a t i o n s a n a l y s i s to
e x p l a i n th e f o r m a t i o n of i n f l a t i o n e x p e c t a t i o n s a n d t h u s is
a b le to d r a w i n f e r e n c e s a b o u t t he b e h a v i o r of t h e n o n
o b s e r v a b l e ex a nt e real r a t e s f r o m t he b e h a v i o r of the
e a s i l y m e a s u r e d e x p o s t re a l r a t e s t h e t w o of w h i c h are
equal u n d e r t h e a s s u m p t i o n s m a d e. By e x t e n d i n g his list of
e x p l a n a t o r y v a r i a b l e s t h a t c o u l d p o t e n t i a l l y e x p l a i n real
ra te m o v e m e n t s , c o n f i r m a t i o n of hi s f i n d i n g s t h a t v a r i a b l e s
o t h e r t h a n l a gg ed i n f l a t i o n a r e e c o n o m e t r i c a l l y
i n s i g n i f i c a n t is made. D i s c u s s i o n of a n u m b e r of o t h e r
r e c e n t a n a l y s e s of real i n t e r e s t m o v e m e n t s (e.g. t he s u p p l y
s h o c k m o d e l of W i l c o x (1983), t h e m o n e y s h o c k m o d e l of
M i s h k i n (1982), th e ' s t a g f l a t i o n ' m o d e l of Fa m a (1982),
etc.) a r e s h o w n to be u n a b l e t o e x p l a i n f a l l i n g real
i n t e r e s t r a t e s in the f a c e of i n c r e a s e d i n f l a t i o n d u r i n g o u r
period. In p a r t i c u l a r a d e t a i l e d c r i t i q u e of t h e F a m a
(1982) s t a g f l a t i o n a n a l y s i s is p r o v i d e d .
Also, F a m a ' s v e r y w e l l - k n o w n w o r k on s h o r t - t e r m r a t es
as p r e d i c t o r s of i n f l a t i o n is u p d a t e d t o i n c l u d e the
i n f l a t i o n a r y 1970s an d e a r l y 1 980s. W h e r e a s m o s t w r i t e r s
h a v e b e e n c o n t e n t to t es t th e s t a n d a r d F i s h e r e f f e c t
e q u a t i o n (or s o m e s l i g h t l y m o d i f i e d v e r s i o n of it) m a k i n g
some s i m p l e p r i o r a s s u m p t i o n s a b o u t t h e n a t u r e of i n f l a t i o n
e x p e c t a t i o n s f o r m a t i o n , an d t h e n d e c i d i n g t h a t t h e d a ta
r e j e c t th e F a m a h y p o t h e s i s (e.g. N e l s o n a nd S c h w e r t (1977),
M i s h k i n (1981), et. a l . ) a u n i q u e a p p r o a c h is t a k e n in t h i s
c h a pter. S p e c i f i c a l l y , th e e n t i r e F a m a a n a l y s i s w h i c h
i n v o l v e s t he s e p a r a t e t e s t i n g f or c o n s t a n c y of t h e real r a t e
a n d m a r k e t e f f i c i e n c y is a p p l i e d t o t h e 1 9 5 3- 7 9 a n d 1 9 5 3 - 8 3
pe r iods. In o t h e r w ords, in t h i s s e c t i o n , r a t h e r t h a n
a s s u m i n g m a r k e t e f f i c i e n c y at t h e o u t s e t , as m a n y a u t h o r s
ha ve done, a nd t h e n a t t r i b u t i n g a n y d e v i a t i o n in
c o - m o v e m e n t s b e t w e e n n o m i n a l y i e l d s a n d i n f l a t i o n to
v a r i a b l e ex a n t e real rates, t he a s s u m p t i o n s of m a r k e t
e f f i c i e n c y an d c o n s t a n t real r a t e s a r e t e s t e d i n d e p e n d e n t l y ,
w i t h s om e f a i r l y s u r p r i s i n g r e s u l t s . A l t h o u g h p r o v i s i o n a l ,
the r e s u l t s o b t a i n e d i n d i c a t e t h a t r ea l r a t es m a y h a v e b e e n
r o u g h l y c o n s t a n t d u r i n g th e r e l e v a n t p e r i o d s b u t t h a t
p e r h a p s t h e U.S. T - b i l l m a r k e t w a s n o t o p e r a t i n g
e f f i c i e n t l y , e v e n in the ' we ak es t" se n s e . T h e s e r e s u l t s a re
s t a t e d v e r y t e n t a t i v e l y as t h e r e a r e s om e t h e o r e t i c a l
p i t f a l l s in t h is t yp e of w ork, s o m e of w h i c h a re d i s c u s s e d
in t he text.
A n o t h e r i n t e r e s t i n g a s p e c t t o C h a p t e r 2 is th e t e s t i n g
for t h e l o n g e r r u n c o - m o v e m e n t s of i n f l a t i o n a n d i n t e r e s t
r at es t h a t is u n d e r t a k e n there. S o m e w h a t d i f f e r e n t r e s u l t s
ar e o b t a i n e d d e p e n d i n g on t he p a r t i c u l a r f i l t e r i n g t e c h n i q u e
used. H o w e v e r it is a r g u e d t h a t t h e L u c a s (1980) a p p r o a c h
is p r e f e r a b l e to the s i m p l e r S u m m e r s (1981) o n e b e c a u s e of
the s u p e r i o r u n d e r l y i n g t h e o r e t i c a l a s s u m p t i o n m a d e
c o n c e r n i n g t h e e x p e c t a t i o n s g e n e r a t i n g p r o c e s s of m a r k e t
p a r t i c i p a n t s . I n t e r e s t i n g l y , w h e r e a s L u c a s i n f e r r e d f r o m
hi s a n a l y s i s a c l o se 1 - for-l r e l a t i o n s h i p b e t w e e n i n f l a t i o n
an d n o m i n a l y ie ld s , he n e v e r t e s t e d f o r it d i r e c t l y ,
s o m e t h i n g w h i c h is d o n e in a n a p p e n d i x t o C h a p t e r 2. Th e r e ,
e v i d e n c e is p r o v i d e d t h at w h i l e l o n g r u n or lo w f r e q u e n c y
c o - m o v e m e n t s b e t w e e n t h e s e v a r i a b l e s a r e i n d e e d close, t h e y
are s i g n i f i c a n t l y less t h a n 1 - f or -l , s p e c i f i c a l l y n o m i n a l
r a t e s do n o t a d j u s t f u l l y to c h a n g e s in i n f l a ti on . T h is
r e s u l t is c o n f i r m e d in a n o t h e r a p p e n d i x t h r o u g h t h e us e of
m o r e f or m a l c r o s s s p ec tr al t e c h n i q u e s wh i c h , to m y
k n o w l e d g e , h a v e no t y e t b e e n a p p l i e d to th e v a r i a b l e s t h a t
are of i n t e r e s t to us. In a n o t h e r a p p e n d i x , it is s h o w n
t h a t w i t h p r o p e r A R I M A m o d e l l i n g of t he t im e s er ie s of
i n f l a t i o n a n d n o m i n a l rates, t h e t h e o r e t i c a l p r e s u m p t i o n of
t h e u n i d i r e c t i o n a l i n f l u e n c e f r o m i n f l a t i o n t o i n t e r e s t
r a t e s is b o r n e out, in c o n t r a s t t o e a r l i e r s t u d i e s w h i c h
i n d i c a t e d a r e v e r s e ' c ausality'.
C h a p t e r 3 r e p r e s e n t s th e f i r s t a t t e m p t to t e s t the
p r e d i c t i o n s of t he l i q u i d i t y m o d e l d i r e c t l y , t h e m o s t
i m p o r t a n t b e i n g t ha t the g r e a t e r t h e ' m o n e y n e s s ' of an a s s e t
t h e m o r e (less) w i l l its real (no m i n a l ) y i e l d be a f f e c t e d by
a c h a n g e in i n f l a t io n. A s e t of g o v e r n m e n t s e c u r i t i e s
i d e n t i c a l in all r e s p e c t s e x c e p t f o r m a t u r i t y l e n g t h is u s e d
in on e a n a l y s i s w h e r e a s in a n o t h e r a s s e t s t h a t s h a r e a
c o m m o n m a t u r i t y p e r i o d b u t d i f f e r in o t h e r m a r k e t a b i l i t y
c h a r a c t e r i s t i c s (and thus t r a d i n g c o s t s) are used. Also, a
c a r e f u l d i s c u s s i o n of the r a t i o n a l e f or the p a r t i c u l a r
r a n k i n g s of a s s e t s g i v e n in t h e c h a p t e r w i t h r e s p e c t to t h e
l i q u i d i t y s e r v i c e s t h e y g e n e r a t e , is p r o v i d e d in th e t e x t in
th e a p p r o p r i a t e sections. A n i m p o r t a n t p o i n t s t r e s s e d in
t h e s e s e c t i o n s c o n c e r n s the n e c e s s i t y of d r a w i n g a
d i s t i n c t i o n b e t w e e n l i q u i d i t y ( d e f i n e d as the a b s e n c e of
t r a n s a c t i o n s costs) and r i s k f a c t o r s in t h e d e t e r m i n a t i o n of
h o l d i n g p e r i o d d i f f e r e n t i a l s .
In o n e s e c t i o n of the c h a p t e r t h e a r g u m e n t is p u t
fo r w a r d , w i t h s o me s u p p o r t i n g e m p i r i c a l e v i d e n c e , t h a t t h e
a p p a r e n t l y a n o m a l o u s b e h a v i o r of e q u i t y and b o n d m a r k e t s in
t h e U.S. d u r i n g t h e 1970s, a s u b j e c t of i n t e n s e d i s c u s s i o n
to t he p r e s e n t day, is e n t i r e l y c o n s i s t e n t w i t h the
p r e d i c t i o n s of t h e l i q u i d i t y m o d e l . In this, as w e l l as in
o t h e r s e c t i o n s , t w o a l t e r n a t i v e p r o x i e s for e x p e c t e d
i n f l a t i o n u s i n g K e y n e s i a n a n d r a t i o n a l e x p e c t a t i o n a l
a s s u m p t i o n s a r e u s e d in t h e e m p i r i c a l a n a l y s e s .
N e a r t he e n d of the c h a p t e r , d i r e c t OLS e s t i m a t i o n of
the p a r a m e t e r s in an e q u a t i o n m a t h e m a t i c a l l y d e r i v e d f r o m
the l i q u i d i t y m o d e l is u s e d to t e s t t h e m o d e l ' s i m p l i c a t i o n
that an a s s e t ' s n o m i n a l h o l d i n g p e r i o d r e t u r n will be less
i n f l u e n c e d by a c h a n g e in i n f l a t i o n t he g r e a t e r is the
a s s e t ' s d e g r e e of s u b s t i t u t a b i l i t y w i t h m oney, w i t h v e r y
f a v o r a b l e r e s u l t s .
C h a p t e r 4 d e a l s w i t h t h e a p p l i c a t i o n of the l i q u i d i t y
m o d e l to the c a p i t a l a s s e t p r i c i n g m o d e l (CAPM) a n a l y s i s to
e x p l a i n s o m e s e e m i n g l y i n c o n s i s t e n t r e s u l t s o b t a i n e d by th e
v a r i o u s C A P M r e s e a r c h e r s . F o r i n s t a n c e , a c o m m o n f i n d i n g is
t h a t t h e i n t e r c e p t of the e m p i r i c a l s e c u r i t y m a r k e t li n e
(SML) is g r e a t e r and the s l o p e t e r m is less t h a n p r e d i c t e d
by t h e t w o - p a r a m e t e r m odel. If s e c u r i t i e s are h e l d
' e f f i c i e n t l y ' (as m o s t s t u d i e s i n d i c a t e is i n d e e d t h e ca s e ) ,
an o v e r - e s t i m a t e d i n t e r c e p t t e r m w i ll led to an u n d e r
e s t i m a t e d s l o p e t e r m and v i c e - v e r s a , a f a c t t h a t has b e e n
o v e r l o o k e d by w r i t e r s in t h i s area. T h e p r i m a r y a r g u m e n t in
C h a p t e r 4 is t h a t t h e a p p a r e n t l y a n o m a l o u s f i n d i n g s of the
C A P M r e s e a r c h e r s has b ee n d u e to t h e e x c l u s i o n of a
l i q u i d i t y f a c t o r in t h e d e t e r m i n a t i o n of e q u i t y r e t u r n s . In
o t h e r w o r d s , th e m e a s u r e d i n t e r c e p t t e r m s for th e e m p i r i c a l
SML a r e t h e p r o p e r on e s w h e n a c c o u n t is t a k e n of the f a c t
t h a t e q u i t i e s are less l i q u i d t h a n T r e a s u r y bi l l s , the
l at t er y i e l d i n g a r e t u r n t h a t is t a k e n t o r e p r e s e n t th e
' ri sk -f r e e ' rate. T h e r e f o r e , t h e l i q u i d i t y p r e m i a on
e q u i t i e s vi s a' v i s T - b i l l s a r e t h e d i f f e r e n c e s b e t w e e n th e
SML i n t e r c e p t s a n d the T -b i l l r a t e s for th e c o r r e s p o n d i n g
p er io ds . It is e a s i e s t to i m a g i n e a s e c u r i t y m a r k e t
h y p e r p l a n e t h a t i n c l u d e s l i q u i d i t y b e i n g m e a s u r e d in th e
t h i r d d i m e n s i o n as o p p o s e d to t h e s t a n d a r d tw o p a r a m e t e r
s e c u r i t y m a r k e t l i n e t h a t s h o w s o n l y t h e r i s k - r e t u r n t r a d e
off. It is a l s o a r g u e d t h a t t h i s l i q u i d i t y f a c t o r is
i d e n t i c a l t o t h a t d e r i v e d f r o m F-H. To e m p i r i c a l l y t e s t
t h i s p r o p o s i t i o n , the e m p i r i c a l S M L i n t e r c e p t s f r o m C A P M
t e s t s u t i l i z i n g f i v e d i f f e r e n t m a r k e t p o r t f o l i o p r o x i e s
(most a n a l y s e s us e the e q u a l l y - w e i g h t e d N Y S E c o m m o n s t o c k
i n d e x al o n e ) a r e c o m p u t e d and f r o m t h e m are s u b t r a c t e d
t h e c o r r e s p o n d i n g r i s k - f r e e r at e s . T h e s e v a l u e s are t a k e n
to be l i q u i d i t y p r e m i a a n d ar e r e g r e s s e d on v a r i a b l e s w h i c h
a c c o r d i n g to th e l i q u i d i t y m o d e l s h o u l d i n f l u e n c e them.
T h i s is d o n e in b o t h a c o n t e m p o r a n e o u s a n a l y s i s and in on e
in w h i c h la r g e p e r i o d - t o - p e r i o d f l u c t u a t i o n s in v a l u e s (a
c o m m o n f e a t u r e of C A P M a n a l y s e s w h i c h d o e s not v i o l a t e an y
of its a s s u m p t i o n s , as e x p l a i n e d in t h e text) a re a t t e n u a t e d
t h r o u g h the a p p l i c a t i o n of a s m o o t h i n g pr o c e s s . B o t h
a n a l y s e s y i e l d f a v o r a b l e r e s u l t s . A ls o , a b a s i c
m e t h o d o l o g i c a l d i s c u s s i o n and c r i t i q u e of the v e r y
i n f l u e n t i a l Roll (1977) w o r k is o f f e r e d in the ch a p t e r .
F i n a l l y , C h a p t e r 5 s u m m a r i z e s a n d d r a w s t o g e t h e r in
s o m e d e t a i l t h e w o r k p r e s e n t e d in t h e f i r s t fo u r c h a p t e r s.
S p e c i a l a t t e n t i o n is p a i d to h i g h l i g h t i n g s o m e of the
t h e s i s ' m o s t i m p o r t a n t an d u n i q u e c o n t r i b u t i o n s .
C H A P T E R 1:
G E N E R A L D I S C U S S I O N O F T H E F I S H E R E F F E C T
A N D T H E M O D E L
I. T he F i s h e r Ef f e c t : D i s c u s s i o n a n d E m p i r i c a l W o r k
T h i s c h a p t e r has a n u m b e r of i m p o r t a n t a i m s a m o n g w h i c h
a r e i n c l u d e d a d i s c u s s i o n of t h e p r e s u m e d t h e o r e t i c a l
r e l a t i o n s h i p b e t w e e n i n t e r e s t r a t e s a n d i n f l a t i o n in b o t h
th e lo n g a n d s h o r t run, t he p r e s e n t a t i o n of t he e m p i r i c a l
e v i d e n c e of o t h e r s on t h e f o r e g o i n g q u e s t i o n a n d a
d e s c r i p t i o n of a m o d e l i n c o r p o r a t i n g t h e l i q u i d i t y
c h a r a c t e r i s t i c s of g o v e r n m e n t s e c u r i t i e s w h i c h a t t e m p t s to
e x p l a i n a r e s u l t g e n e r a l l y f o u n d in t e s t s of th e
r e l a t i o n s h i p b e t w e e n the t wo v a r i a b l e s w h i c h is, as w e s h a l l
see, r e j e c t i o n of the s u p e r n e u t r a l i t y h y p o t h e s i s , i.e., t h e
b e l i e f t h a t i n f l a t i o n w i l l n o t a f f e c t real i n t e r e s t r a t e s in
the long run.
In m o s t of the r e l a t i v e l y m o r e r e c e n t a n a l y s e s , t h e
s u p e r n e u t r a l i t y h y p o t h e s i s is b a s e d o n t h e t h e o r e t i c a l m o d e l
of S i d r a u s k i (1967) w h i c h i n c o r p o r a t e s as o n e of its m o r e
i m p o r t a n t f e a t u r e s a g i v e n m a r g i n a l r a t e of t i m e p r e f e r e n c e
to w h i c h is e q u a t e d the s t e a d y s t a t e m a r g i n a l p r o d u c t of
ca p i t a l . As t h e r a te of t i m e p r e f e r e n c e w i ll b e u n a f f e c t e d
b y c h a n g e s in i n f l at io n, so w il l b e t h e m a r g i n a l p r o d u c t of
ca p i t a l . G i v e n t he a d d i t i o n a l a s s u m p t i o n s of p e r f e c t l o n g
-ru n f o r e s i g h t on the p a r t of t h e r e p r e s e n t a t i v e h o u s e h o l d as
w e l l as c o m p l e t e s u b s t i t u t a b i l i t y b e t w e e n c a p i t a l a n d b o nds,
it f o l l o w s t h a t t h e real r a t e of i n t e r e s t is eq u a l t o th e
m a r g i n a l p r o d u c t of c a p i t a l a nd it t o o w i ll be i n d e p e n d e n t
of th e i n f l a t i o n r a t e in th e lo n g run.'*' F u r t h e r m o r e , as
s t a n d a r d m o n e t a r y t h e o r y p r e d i c t s t h a t the s t e a d y s t a t e
i n f l a t i o n r a t e w i l l be e q u al t o t h e r a t e of m o n e t a r y g r o w t h
th e s u p e r n e u t r a l i t y of m o n e y in a l o n g - r u n a n a l y s i s
l o g i c a l l y f o l lo ws .
S o m e w r i t e r s h a v e a r g u e d t h a t a n i n v e r s e r e l a t i o n s h i p
b e t w e e n c h a n g e s in e x p e c t e d i n f l a t i o n a n d real r a t e s in t h e
s h o r t - r u n c o u l d p o s s i b l y b e e x p l a i n e d b y i n v o k i n g th e
M u n d e l l - T o b i n a n a l y s i s w h i c h is t h e f o l l o w i n g : an i n c r e a s e
in e x p e c t e d i n f l a t i o n r a i s e s t he o p p o r t u n i t y c os t s of
h o l d i n g m o n e y b a l a n c e s w h i c h c a u s e s p e o p l e t o s h i f t o u t of
m o n e y a n d i n t o i n t e r e s t b e a r i n g a s s e t s . T hi s c a u s e s the
e q u i l i b r i u m e x p e c t e d r e t u r n o n t h e s e a s s e t s to d ec l i n e . T he
s u b s e q u e n t r e d u c t i o n in t h e " c o st of c a p i t a l " w i l l c a u se
firms e n g a g e d in a c a p it al e x p e n d i t u r e s d e c i s i o n - m a k i n g
p r o c e s s to a c q u i r e m o r e c a p it al , t h u s d r i v i n g d o w n th e
e c o n o m y - w i d e m a r g i n a l p r o d u c t of c a p i t a l . Th i s is m o s t
c l e a r l y s ee n w i t h i n t he c o n t e x t of t h e n e o - c l a s s i c a l g r o w t h
mo d e l . If, as in m o s t a na l y s e s , c o n s u m p t i o n is p o s i t i v e l y
r e l a t e d to w e a l t h t h e n the i n d u c e d r e d u c t i o n in d e s i r e d real
m o n e y h o l d i n g s b r o u g h t a b o u t b y a n i n c r e a s e in i n f l a t i o n
w i ll c a u s e c o n s u m p t i o n at e a c h i n c o m e le v e l to fall a n d t h u s
s a v i n g s to rise. H o w e v e r t h i s w h o l e a n a l y s i s r e l i e s g r e a t l y
on a f a i r l y s u b s t a n t i a l real b a l a n c e e f f e c t on c o n s u m p t i o n
and s a v i n g s w h i c h has not b e e n s h o w n to exist, at l e a s t in
the U.S. w i t h its l o w and v e r y s t a b l e s a v i n g s rates. A
p o t e n t i a l a l t e r n a t i v e a pp ro ac h, a l t h o u g h p e r h a p s o n e n o t
w i t h o u t its o w n p r o b l e m s (see C h a p t e r 3), w o u l d be t o a s s u m e
th a t t h e r a t e of t i me p r e f e r e n c e is p o s i t i v e l y r e l a t e d to
w e a l t h a n d t h a t m o n e y and c a p i t a l a r e c o m p l e m e n t a r y g o o d s in
p r o d u c t i o n . As real m o n e y h o l d i n g s a r e r e d u c e d as a
c o n s e q u e n c e of the i n c r e a s e in i n f l a t i o n , t h e m a r g i n a l
p r o d u c t of c a p i t a l wi l l d e c l i n e t h u s r e d u c i n g the d e s i r e d
c a pi ta l stock. H ow e v e r , the r e d u c t i o n in c a p i t a l w i l l s t o p
s ho rt of t h e a m o u n t n e c e s s a r y t o e q u a t e c a p i t a l ' s n e w
m a r g i n a l p r o d u c t t o the o l d le v e l b e c a u s e of the d e c r e a s e in
the r at e of t i m e p re f e r e n c e .
Th e f o l l o w i n g s e c t i o n s u m m a r i z e s m o s t of the m o r e
i m p o r t a n t w o r k d o n e in t e s ts of t h e F i s h e r e f f e c t o v e r
a p p r o x i m a t e l y th e last d ec a d e , f o c u s i n g some a t t e n t i o n on
some v e r y r e c e n t w o r k w h i c h s e e k s t o e x p l a i n its a p p a r e n t
f a il ur e in t h e U.S. e c o n o m y t h a t t h e v a s t m a j o r i t y of
r e s e a r c h e r s in th i s ar e a h a v e d i s c o v e r e d .
In o r d e r to e m p i r i c a l l y t e s t fo r the p r e s e n c e of a full
F i s h e r e f fe ct , m o s t w r i t e r s h a v e i m p l i c i t l y m o d i f i e d t h e
s t a n d a r d F i s h e r r e l a t i o n s h i p g i v e n in (1)
(1) R t = + ir^_ + e t
(where R t ancj a ar e the n o m i n a l a n d r e a l i n t e r e s t r a t e s e
r e s p e c t i v e l y a n d th e e x p e c t e d i n f l a t i o n rate, tt ±s a s s u m e d
to be s t a t i s t i c a l l y i n d e p e n d e n t of t h e e r r o r term) t o b e c o m e
(2) Rt = a +0Tr e + e
w h e r e p is a p a r a m e t e r m e a s u r i n g t h e e x t e n t of the F i s h e r
effect. An a p p r o a c h u s e d b y a n u m b e r of r e s e a r c h e r s in t he
late 1960s a n d e a r l y 1 970s w a s t o u s e s u r v e y d a t a of
i n f l a t i o n a r y e x p e c t a t i o n s , s p e c i f i c a l l y th e d a t a c o l l e c t e d
s e m i - a n n u a l l y b y J o s e p h L i v i n g s t o n , a f i n a n c i a l c o l u m n i s t ,
as a p r o x y fo r t h e e x p e c t e d i n f l a t i o n v a r i a b l e . A l t h o u g h
the t e c h n i q u e of u s i n g s u r v e y d a t a s e e m e d to fall i n t o
d i s r e p u t e d u r i n g th e e a r l y 19 7 0 s (for v a r i o u s r e a s o n s so m e
of w h i c h a r e d i s c u s s e d be l o w ) t h e r e h a s b e e n a r e c e n t
r e s u r g e n c e of i n t e r e s t in the u s e of s u c h data, an i n t e r e s t
w h i c h is r e l a t e d to t h e p r e s e n t p o p u l a r i t y of r a t i o n a l
e x p e c t a t i o n s m o d e l s . T h e a r g u m e n t f o r t h e us e of s u c h d a t a
b y a d v o c a t e s of r a t i o n a l e x p e c t a t i o n s t e c h n i q u e s is
e s s e n t i a l l y t h a t a g e n t s us e c e r t a i n d e c i s i o n r u l e s in the
f o r m a t i o n of t h e i r e x p e c t a t i o n s , r u l e s w h i c h a r e in s o m e
s ense e m b o d i e d in t h e i r r e p o r t e d f o r e c a s t s b u t w h i c h c a n n o t
2
be o b s e r v e d f u l l y b y t h e m a c r o e c o n o m e t r i c i a n . T h e r e f o r e
t he y a r g u e t h a t s u r v e y d a t a a r e i n t r i n s i c a l l y m o r e
m e a n i n g f u l t h a n s u c h a l t e r n a t i v e a p p r o a c h e s as using, for
e x a m p l e , an a r b i t r a r i l y s e l e c t e d n u m b e r of l a g g e d v a l u e s of
i n f l a t i o n w i t h e q u a l l y a r b i t r a r y w e i g h t s a t t a c h e d t o t h e m as
an i n f l a t i o n e x p e c t a t i o n s p roxy. A l t h o u g h t h i s is a v e r y
c o n t e n t i o u s i ssue, a n d b e y o n d t h e s c o p e of th e p r e s e n t wo r k ,
o c c a s i o n a l a r g u m e n t s c o n c e r n i n g t h e a d v a n t a g e s as w e l l as
the d i s a d v a n t a g e s of u s i n g s u r v e y d a t a p u t f o r t h b y v a r i o u s
w r i t e r s w i l l b e n o t e d as t h e i r w o r k is r e v i e w e d .
G i b s o n (1972) an d P y l e (1972) c o m e to th e c o n c l u s i o n
th at n ot o n l y do o b s e r v e d p r i c e e x p e c t a t i o n s of t h e
L i v i n g s t o n v a r i e t y c o n t r i b u t e s i g n i f i c a n t l y to the
d e t e r m i n a t i o n of n o mi na l i n t e r e s t r a t e s but, in a dd it io n,
t h a t th e c o e f f i c i e n t on e x p e c t e d i n f l a t i o n is s u b s t a n t i a l l y
b e l o w u n i t y ( r o ug h ly .65). H o w e v e r L a h i r i (1976) a t t r i b u t e s
the f i n d i n g of a l o w c o e f f i c i e n t o n t h e p r i c e e x p e c t a t i o n s
v a r i a b l e to a n " e r r o r s in v a r i a b l e s " p r o b l e m , a p o s s i b i l i t y
a l l u d e d to b y b o t h of the a b o v e a u t h o r s . H o w e v e r , e v e n
a f t e r a p p l y i n g his c o r r e c t i v e t e c h n i q u e s a m o n g w h i c h are
i n c l u d e d a t w o - s t a g e le a s t s q u a r e s e s t i m a t i o n of t h e b a s i c
i n t e r e s t r a t e e q u a t i o n f r o m a r e d u c e d f o r m m o d e l of i n t e r e s t
r a t e a n d p r i c e level e x p e c t a t i o n s f or ma t i o n , he f i n ds t h a t
the c o e f f i c i e n t on e x p e c t e d i n f l a t i o n is still s i g n i f i c a n t l y
b e l o w un i t y , a l t h o u g h a b i t h i g h e r t h a n t h a t f o u n d b y G i b s o n
a n d Pyle.
C a r g i l l (1976) a n d C a r l s o n (1975) p o i n t o ut t ha t
L i v i n g s t o n m a k e s a d j u s t m e n t s t o h i s s u r v e y d a t a b e f o r e
p u b l i s h i n g t h e m a n d C a r l s o n n o t e s t h a t d i f f e r e n c e s b e t w e e n
the p u b l i s h e d f o r e c a s t s a n d t h e a c t u a l a r i t h m e t i c a v e r a g e of
the r e s p o n d e n t s ' e s t i m a t e s v a r y m a r k e d l y o v e r time. C a r g i l l
r e c o m p u t e s t h e F i s h e r e q u a t i o n u s i n g t h e a v e r a g e of t h e
r e s p o n d e n t s ' f o r e c a s t s of i n f l a t i o n f o r e a c h t i m e p e r i o d a n d
c o n c l u d e s t h a t t h e e v i d e n c e in f a v o r of a c l o s e r e l a t i o n s h i p
b e t w e e n n o m i n a l r a t e s a n d e x p e c t e d i n f l a t i o n is f a i r l y we a k .
In an i n t e r e s t i n g o f f s h o o t of t h e b a s i c a p p r o a c h of
u s i n g th e L i v i n g s t o n s u r v e y d a t a as a p r o x y for e x p e c t e d
i n f l a t i o n , B o m b e r g e r and F r a z e r (1981) use t h e s t a n d a r d
d e v i a t i o n s of the i n d i v i d u a l p e r i o d f o r e c a s t s in a r e d u c e d
f o r m i n t e r e s t r a t e e q u a t i o n as a p r o x y for the d e g r e e of
i n f l a t i o n u n c e r t a i n t y w i t h t he e v i d e n c e i n d i c a t i n g a
s i g n i f i c a n t l y n e g a t i v e i n f l u e n c e of t h i s u n c e r t a i n t y
v a r i a b l e . T h i s r e s u l t is in a c c o r d a n c e w i t h t h e p r e d i c t i o n
of the m o d e l of B l e j e r a n d E d e n (1979) an d c o u l d h e l p
e x p l a i n why, in the c o n t e x t of t h e i r w ork, so m a n y a u t h o r s
h a v e f ou n d an u n d e r a d j u s t m e n t of n o m i n a l ra t e s to i n f l a t i o n .
The b a s i c a r g u m e n t is as f o ll o w s : S u p p o s e t h e p r o p e r
s p e c i f i c a t i o n of the F i s h e r e q u a t i o n is
i=b + b n + b~ v a r 7T w h e r e t h e last v a l u e is the
o 1 2
e x p e c t e d v a r i a n c e of i n f l a t i o n . In o t h e r words, u n c e r t a i n t y
is e x p l i c i t l y i n t r o d u c e d . T h a t e s t i m a t e of the p a r a m e t e r o n
e x p e c t e d i n f l a t i o n is thus'IS^ = ^l + ^2 C 1 w ^ ere c \ -*-s c o e f f i c i e n t on e x p e c t e d i n f l a t i o n w h e n t h e ac t u a l v a r i a n c e
of i n f l a t i o n is r e g r e s s e d on it. If t h e a s s u m p t i o n is m a d e
t h a t i n f l a t i o n ' s v a r i a n c e i n c r e a s e s d i r e c t l y w i t h its level
( e v i d e n c e t h a t t h i s has i n d e e d b e e n the c a s e d u r i n g o u r
s a m pl e p e r i o d w i ll be p r e s e n t e d b e l o w ) a n d if b
2
< 0, t h e nb^ will b e d o w n w a r d b ia s e d . A s i m i l a r a r g u m e n t is o f f e r e d
by K o c h i n (1982). H o w e v e r t h e r e is r e a s o n to b e l i e v e t h a t
this p a r t i c u l a r p o t e n t i a l e x p l a n a t i o n m a y not be a p p r o p r i a t e 3
for o u r p e r i o d of i n t e r e s t. T e s t s i n v o l v i n g the use of
a l t e r n a t i v e p r o x i e s for t h e e x p e c t e d r a t e of i n f l a t i o n fall
into b a s i c a l l y t w o g r o u p s , t h o s e u s i n g so m e d i s t r i b u t e d lag
of p a s t i n f l a t i o n r a t e s as the p r o x y and v a r y i n g p r o x i e s
a p p r o a c h p r e - d a t e s the s u r v e y d a t a o n e c o m p a r e d to w h i c h it
is u s u a l l y r e g a r d e d as i n f e r i o r g i v e n t h e n e c e s s a r y
a r b i t r a r i n e s s i n v o l v e d in the s e l e c t i o n of the lag l e n g t h to
be used. T h e m o s t w e ll k n o w n w o r k i n t hi s a r e a w as d o n e b y
F i s h e r h i m s e l f w h o w a s u n a b l e t o c o n f i r m th e e x i s t e n c e of
a n y F i s h e r e f f e c t i n s t e a d f i n d i n g t h a t n o m i n a l i n t e r e s t
r at es c h a n g e d b y less t h a n .25% for e v e r y o n e p e r c e n t a g e
p o i n t c h a n g e in e x p e c t e d i n f l a t i o n .
A v e r y i n g e n i o u s a p p r o a c h t o t h e s t u d y of a k e y f e a t u r e
i m p l i c i t in m o s t a n a l y s e s of th e F i s h e r eff e c t , the
c o n s t a n c y of t he e x a n t e real r a t e of i n t e r e s t (the e x p e c t e d
real r e t u r n f r o m h o l d i n g an i n s t r u m e n t ) w a s u n d e r t a k e n b y
M i s h k i n (1981). E s s e n t i a l l y h i s t e c h n i q u e i n v o l v e s u s i n g
the d e t e r m i n a b l e ex p o s t real r a t e s (the n o m i n a l i n t e r e s t
r a t es m i n u s a c t u a l i n fl at io n) to i n f e r b e h a v i o r a b o u t t h e
u n o b s e r v a b l e e x a n t e real i n t e r e s t rate. M i s h k i n
i l l u s t r a t e s t h a t t h i s is a p e r f e c t l y a c c e p t a b l e t e c h n i q u e
u n d e r c e r t a i n a s s u m p t i o n s i m p l i c i t in t he r a t i o n a l
e x p e c t a t i o n s a p p r o a c h. As it r e p r e s e n t s p r o b a b l y t h e m o s t
s o p h i s t i c a t e d r a t i o n a l e x p e c t a t i o n s t e s t (albeit i n d i r e c t )
of the b a s i c v a l i d i t y of t h e F i s h e r e f f e c t , w e w i ll a d o p t
its b a s i c a p p r o a c h , w i t h a d i f f e r e n t d a t a set, in C h a p t e r 2
w h e n o u r o w n t e s t s of t h e F i s h e r e f f e c t a r e u n d e r t a k e n .
M o r e r e l e v a n t to ou r c u r r e n t c o n c e r n , h ow e v e r , is t h a t
M i s h k i n ' s r e s u l t s n o t o n l y t e n d t o c o n f i r m the
u n d e r a d j u s t m e n t h y p o t h e s i s b u t a l s o p r o v i d e e v i d e n c e f or t h e
d o m i n a n t i n f l u e n c e of i n f l a t i o n a r y e x p e c t a t i o n s on n o m i n a l
rates, i.e., t he la c k of e m p i r i c a l s u p p o r t for th e b e l i e f
th a t t h o s e v a r i a b l e s o t h er t h a n i n f l a t i o n w h i c h are
g e n e r a l l y t h o u g h t to i n f l u e n c e r e a l r a t e s a c t u a l l y do.
N e v e r t h e l e s s , as F r i e d a n d H o w i t t (1983) p o i n t out, a
f a i l u r e t o f i n d a n y e v i d e n c e for a f u l l F i s h e r e f f e c t u s i n g
s h o r t r u n d a t a d o e s n ot p r e c l u d e t h e v a l i d i t y of a n y l o n g
-r u n s u p e -r n e u t -r a l i t y h y p o t h e s i s . S u m m e r s ( 1981 ),( 1983 )
a d d r e s s e s t h i s v e r y i s s ue b y u t i l i z i n g s p e c t r a l a n a l y s i s t o
f il te r o ut s h o r t - t e r m c o - m o v e m e n t s of i n t e r e s t r a t e s a n d
p r i c e s u s i n g v a r y i n g f il t e r l e n g t h s a n d c o n c l u d e s t h a t o n l y
d u r i n g t he p o s t - W W I I er a d o e s t h e r e s e e m t o be a n y
s i g n i f i c a n t r e l a t i o n s h i p at all b e t w e e n th e t w o v a r i a b l e s .
Again, t h e f i n d i n g of a less t h a n u n i t c o e f f i c i e n t (for t he
1 9 48-79 p e ri od ) of r o u g h l y .6 is t h e r e s u l t . L u c a s (1980)
uses a t w o - s i d e d f i l t e r to c o m p a r e t h e lo n g s w i n g s in
i n t e r e s t r a t e s a n d m o n e y g r o w t h (not i n f l a t i o n ) a nd finds,
v e r y s i g n i f i c a n t l y , a c o e f f i c i e n t s u f f i c i e n t l y c l o s e to
unity. B o t h of t he a b o v e w o r k s w i l l b e d e a l t w i t h in far
g r e a t e r d e t a i l la t e r w h e n e a c h of t h e p a r t i c u l a r f i l t e r i n g
t e c h n i q u e s w i l l be used, a n d c o m p a r i s o n s d r a w n b e t w e e n them,
in a c h a p t e r t h a t d e a l s w i t h t h e p r e s e n t w o r k ' s a n a l y s i s of
the i n f l a t i o n - i n t e r e s t r a t e r e l a t i o n s h i p .
II. T a x e s a n d th e F i s h e r E f f e c t
A v e r y i m p o r t a n t r e l a t e d a s p e c t t h a t m u s t b e c o n s i d e r e d
in a n y a n a l y s i s of the i n f l a t i o n - i n t e r e s t r a t e r e l a t i o n s h i p
u s i n g m o d e r n d a t a is t h at of t a x a t i o n of n o m i n a l r e t ur ns .
of course, t h a t a c o e f f i c i e n t of s u b s t a n t i a l l y g r e a t e r t h a n
u n i t y w o u l d b e r e q u i r e d for a full F i s h e r e f f e c t to be
o pe ra t i v e , i.e., for t h e r e to b e a c o n s t a n t a f t e r - t a x real
i n t e r e s t rate. T h e b a s i c w o r k on t a x - a d j u s t e d real r e t u r n s
wa s d o n e b y D a r b y (1975) w h o a s s u m e d a s i m p l e e c o n o m y - w i d e
m a r g i n a l t a x rate. G a n d o l f i (1976) e x t e n d s s o m e w h a t the
b a s i c D a r b y a n a l y s i s b y d e v e l o p i n g a s i m p l e m o d e l of s a v i n g
an d c a p i t a l a c c u m u l a t i o n a n d i l l u s t r a t e s t h a t g i v e n th e
a s s u m p t i o n of a r e l a t i v e l y s t a b l e e q u i l i b r i u m real r a t e t he
full F i s h e r e f f e c t w i l l o p e r a t e o n l y u n d e r c e r t a i n
c on d i t i o n s . In hi s mo d e l , full a d j u s t m e n t o c curs, in t h e
p r e s e n c e of a p o s i t i v e m a r g i n a l t a x rate, o n l y if s a v i n g s
are c o m p l e t e l y u n r e s p o n s i v e to c h a n g e s in the real r e t u r n o n
s a v i n g s or if t h e re a l i n t e r e s t r a t e e l a s t i c i t y of
i n v e s t m e n t d e m a n d a p p r o a c h e s i n f i n i t y .
F e l d s t e i n (1976) f u r t h e r d e v e l o p s th e a n a l y s i s by
a l l o w i n g fo r t h e e x i s t e n c e of t w o s e p a r a t e t ax rates, one
for c o r p o r a t e a n d o n e for p e r s o n a l in c o m e . Hi s m o d e l is
f u r t h e r d i f f e r e n t i a t e d f r o m G a n d o l f i ' s b y th e f e a t u r e t h a t
e v e n in t h e a b s e n c e of a ny t a x e s a t al l in the e c o no my , t h e
full F i s h e r e f f e c t w i l l o p e r a t e o n l y u n d e r th e c o n d i t i o n of
ze r o i n t e r e s t r a t e e l a s t i c i t y of t h e d e m a n d f o r real m o n e y
b a l a n c e s . L e v i a n d M a k i n (1978) a r g u e t h a t t h e u s u a l
p r o c e d u r e of c o n s i d e r i n g e i t h e r t h e F i s h e r or D a r b y
h y p o t h e s i s in i s o l a t i o n is i n a p p r o p r i a t e a n d ca n le a d t o t h e
i n c o r r e c t i n f e r e n c e t h a t th e f i n d i n g of a u n i t c o e f f i c i e n t
o n e x p e c t e d i n f l a t i o n i m p l i e s l i t t l e o r no i m p a c t of
e q u i l i b r i u m m o d e l in w h i c h th e D a r b y f o r m of the F i s h e r
e q u a t i o n is o n e r e d u c e d f or m r e l a t i o n s h i p t h e y s h o w t h a t
i n c r e a s e s in e x p e c t e d i n f l a t i o n w i l l u n a m b i g u o u s l y d e c r e a s e
a f t e r - t a x re a l y i e l d s , a r e s u l t w h i c h is c o n s i s t e n t w i t h
full, u n d e r or o v e r a d j u s t m e n t of n o m i n a l r a t e s to i n f l a t i o n .
T o f i n i s h the f o r e g o i n g l i t e r a t u r e r e v i e w on t h e t a x
-a d j u s t e d F i s h e r e f f e c t (or D -a r b y e f f e c t ) , it s h o u l d -a l s o b e
n o t e d t h a t S u m m e r s (1981) r e m i n d s t h e r e a d e r s of th e
d i f f i c u l t i e s a s s o c i a t e d w i t h s e l e c t i n g t he a p p r o p r i a t e
m a r g i n a l t a x r a t e to b e u s e d in a n y e m p i r i c a l a n a l y s i s of
th e p h e n o m e n o n . P a r t l y fo r t hi s r e a s o n a nd p a r t l y fo r the
f a c t t ha t w e ar e m o r e c o n c e r n e d in t he p r e s e n t w o r k w i t h
t e s t i n g for a g e n e r a l u n d e r a d j u s t m e n t of n o m i n a l r a t e s to
i n f l a t i o n t h a n w e a r e w i t h its p r e c i s e n u m e r i c a l
m e a s u r e m e n t , t a x e f f e c t s w i l l be i g n o r e d in C h a p t e r 2 w h i c h
d e a l s w i t h o ur o w n a n a l y s i s of th e i n f l a t i o n - i n t e r e s t r a t e
r e l a t i o n s h i p . Of c o urse, if t h e u n d e r a d j u s t m e n t h y p o t h e s i s
is c o n f i r m e d w i t h a m o d e l w h i c h d e l e t e s t a x e s it w o u l d be
m o r e s t r o n g l y so in o ne w h i c h i n c o r p o r a t e s ta x e f f e c t s . F or
e x a m p l e if w e a ss u m e , as d i d F e l d s t e i n a n d S u m m e r s (1979)
a nd S u m m e r s (1981), a m a r g i n a l t a x r a t e f a c e d b y t h e h o l d e r s
of i n t e r e s t b e a r i n g c o r p o r a t e a s s e t s of 33% t h e n it f o l l o w s
t h at n o m i n a l r a t e s w o u l d h a v e to r i s e 1.5 p e r c e n t a g e p o i n t s
for e v e r y p e r c e n t a g e p o i n t i n c r e a s e in i n f l a t i o n to m a i n t a i n
a c o n s t a n t re a l a f t e r t a x i n t e r e s t r a t e ( d r / d m = 1 / 1 -t w h e r e
t is th e a p p r o p r i a t e m a r g i n a l t a x r a t e ) . H o w e v e r t h e a b o v e
a n a l y s i s w o u l d b e c o r r e c t o n l y in t h e c a s e w h e r e t h e r e w a s
l it t l e d i s p e r s i o n in the m a r g i n a l t ax r a t e s f a c e d by
r e c i p i e n t s of i n t e r e s t income. A l t h o u g h the a b o v e a u t h o r s
t a k e a c c o u n t of the g e n e r a l l y h i g h e r m a r g i n a l r a t e s f a c e d b y
c o r p o r a t i o n s as o p p o s e d to i n d i v i d u a l s , it is n e c e s s a r y to
r e m e m b e r t h a t u n d e r the f a i r l y p r o g r e s s i v e f e de ra l i n c o m e
t a x s y s t e m in the U.S., e f f e c t i v e m a r g i n a l t a x r a t e s v a r y
c o n s i d e r a b l y a m o n g i n d i v i d u a l s t h e m s e l v e s . T h u s if t h e r e
has b e e n s o me s h i f t in o w n e r s h i p of i n t e r e s t b e a r i n g a s s e t s
a m o n g t h e v a r i o u s i n c o m e g r o u p s i n t h e e c o n o m y , it w o u l d be
d i f f i c u l t to i n c o r p o r a t e a s i n g l e m a r g i n a l ta x r a t e t h a t
w o u l d p r o v i d e the r e q u i r e d d e g r e e of a d j u s t m e n t of n o m i n a l
r a t e s to i n f l a t i o n (to m a i n t a i n c o n s t a n t real a f t e r t ax
rat e s ) , e s p e c i a l l y in a l o n g e r t e r m a n a l y s i s . Of c o urse,
c h a n g e s in t he t a x r a t e s t h e m s e l v e s (e.g. t h e 1981 R e a g a n
ta x cuts) w o ul d, c e t e r i s p a r i b u s , h a v e s o m e i n f l u e n c e o n t h e
r e q u i r e d d e g r e e of a d j u s t m e n t .
To f u r t h e r i l l u s t r a t e t he c o m p l i c a t i n g f a c t o r t h a t t h e
t a x s y s t e m i t s e l f is n o t n e u t r a l t o i n f l a t i o n , c o n s i d e r t h e
f o l l ow in g : s u p p o s e an i n d i v i d u a l w e r e to p u r c h a s e w i t h
b o r r o w e d f u n d s a p i e c e of c a p i t a l , or a c l a i m to c a p i t a l ,
for i n v e s t m e n t p u r p o s e s in a n e c o n o m y w i t h a g i v e n r e a l r a t e
a n d o n e in w h i c h n o m i n a l i n t e r e s t r a t e s a d j u s t e d f r e e l y to
m a i n t a i n re a l a f t e r t a x i n t e r e s t p a i d at some c o n s t a n t level
in t h e f a c e of i n f l at i on . T h i s i n d i v i d u a l w o u l d still be
r e q u i r e d t o p a y t a x on t h e i n c r e a s e in t h e n o m i n a l v a l u e of
h i s c a p i t a l b r o u g h t a b o u t b y i n f l a t i o n a n d th u s w o u l d n o t be
s a t i s f i e d w i t h an a r r a n g e m e n t t h a t w o u l d m a i n t a i n a c o n s t a n t
a f t e r t a x r e a l r a t e to b e r e c e i v e d b y him. O n th e o t h e r
hand, w e r e he to d e v o t e the b o r r o w e d f u n d s to o b t a i n i n g
'psychic" i n c o m e (e.g. a v a c a t i o n ) t h a t w o u l d n o t be s u b j e c t
to c a p i t a l g a i n s t ax a t i o n , s u c h an a r r a n g e m e n t w o u l d
p r o b a b l y b e a c c e p t a b l e to him.
A f u r t h e r d i f f i c u l t y a r i s e s w h e n a l l o w a n c e is m a d e for
the t a x a t i o n of d i f f e r e n t f o r m s of i n c o m e . If, fo r e x a m p l e ,
the t a x a t i o n of e q u i t y i n c o m e is a d d e d t o the a n a l y s i s (e.g.
as in S u m m e r s (1981), H e n d e r s h o t t (1981) a n d F e l d s t e i n a n d
S u m m e r s (1979) ) it is n e c e s s a r y to m o d i f y the s i m p l e D a r b y
a n a l y s i s b y r e p l a c i n g u n i t y in t h e n u m e r a t o r w i
