The Economic
and Social Review,
Vol. 15, No. 1, October
1983,
pp.
57-68
House Prices, Inflation and the Mortgage
Market
D. RODNEY THOM*
University
College,
Dublin
Abstract: This paper presents an analysis of house prices using quarterly Irish data over the period
1971-1980. Evidence is provided to support the hypotheses that real house prices are significantly
influenced by the cost and availability of mortgage credit, the design of the mortgage instrument and the
tax advantage of owner-occupation. Special attention is given to the role played by inflation which,
when acting in concert with the tax and mortgage systems, affects the demand for housing services and
real house prices.
I INTRODUCTION
T
his p a p e r p r e s e n t s a n a n a l y s i s o f r e a l h o u s e p r i c e s i n I r e l a n d w i t h s p e c i a l
reference t o the role played b y i n f l a t i o n , the t a x system and the t y p e o f
mortgage instrument
countries,
geneity
used t o finance house purchase. Evidence f r o m other
p r i n c i p a l l y t h e U S a n d U K , suggests t h a t t h e t r a d i t i o n a l h o m o ­
assumption normally imputed
to consumer demand functions
n o t b e v a l i d i n t h e case o f h o u s i n g . (See, f o r e x a m p l e , B u c k l e y a n d
(1982),
Follain (1982)
and
Kearl (1979).)
This
may
Ermish
assumption implies
that
a n t i c i p a t e d i n f l a t i o n is n e u t r a l w i t h r e s p e c t t o c o n s u m p t i o n so t h a t a n i n f l a t i o n
w h i c h leaves r e l a t i v e p r i c e s a n d r e a l i n c o m e s u n c h a n g e d has n o e f f e c t o n c o n ­
s u m p t i o n decisions.
*This paper was supported by a grant from the Committee for Social Science Research in Ireland for
which the author expresses his gratitude. Thanks are also due to Mark Wynne and Lore Hayes for
assistance with data collection and to two anonymous referees for comments on earlier drafts. The
usual disclaimer applies.
I n t h e case o f h o u s i n g a t least t h r e e a r g u m e n t s h a v e b e e n a d v a n c e d t o s h o w
t h a t w h e n n o m i n a l i n t e r e s t rates rise w i t h i n f l a t i o n , i n s t i t u t i o n a l aspects o f
the tax system and the mortgage market m a y combine to invalidate the
n e u t r a l i t y p o s t u l a t e . F i r s t , u n d e r t h e present t a x system mortgage interest
p a y m e n t s are d e d u c t i b l e against t a x b u t t h e c a p i t a l gains a n d i m p u t e d i n c o m e
from
o w n e r - o c c u p a t i o n are t a x f r e e . I f i n t e r e s t rates r e s p o n d t o
inflation
then granting t a x relief o n interest payments together w i t h e x e m p t i o n for
c a p i t a l gains m a y a l t e r t h e r e a l a f t e r - t a x c o s t o f h o u s i n g c a p i t a l a n d , c o n ­
s e q u e n t l y , t h e d e m a n d f o r h o u s i n g services, e v e n i f i n f l a t i o n is a n t i c i p a t e d
a n d r e l a t i v e p r i c e s are c o n s t a n t .
S e c o n d , i n f l a t i o n m a y also a f f e c t h o u s i n g d e m a n d v i a i t s i m p a c t o n t h e
t y p e o f mortgage i n s t r u m e n t used i n house purchase. T h e m a j o r i t y o f m o r t ­
gages are o f t h e v a r i a b l e i n t e r e s t - r a t e t y p e w h i c h , at a g i v e n i n t e r e s t r a t e ,
f i x e s t h e n o m i n a l v a l u e o f gross r e p a y m e n t s o v e r t h e l i f e o f t h e m o r t g a g e .
W h e n t h e i n t e r e s t r a t e rises, m o n t h l y r e p a y m e n t s also rise b u t i n a d i s p r o ­
p o r t i o n a t e m a n n e r . F o r e x a m p l e , consider a 25 year mortgage o f £ 1 0 , 0 0 0 .
W i t h zero i n f l a t i o n a n d a n o m i n a l interest rate o f 3 per cent a n n u a l repay­
ments w o u l d equal £ 5 7 4 . A t a 2 per cent i n f l a t i o n rate a n d a 5 per cent
n o m i n a l i n t e r e s t r a t e a n n u a l r e p a y m e n t s w o u l d increase b y 2 4 p e r c e n t t o
£ 7 0 9 . H e n c e , e v e n i f i n f l a t i o n is c o r r e c t l y a n t i c i p a t e d a n d n o m i n a l i n c o m e s
are a d j u s t e d a c c o r d i n g l y , t h e r e a l c o s t o f a m o r t g a g e as p e r c e i v e d b y t h e
o w n e r - o c c u p i e r m a y rise s i g n i f i c a n t l y .
T h i r d , e v e n t h o u g h i n f l a t i o n m a y increase t h e r e a l v a l u e o f i n i t i a l r e p a y ­
m e n t s , a rise i n a n t i c i p a t e d i n f l a t i o n also i m p l i e s a faster d e c l i n e i n t h e reeil
value o f f u t u r e repayments w i t h the consequence t h a t the real b u r d e n o f the
mortgage
falls m o r e r a p i d l y . T h i s e f f e c t arises because t h e c o n v e n t i o n a l
mortgage fixes repayments i n n o m i n a l terms and the rate o f decline i n their
r e a l v a l u e is g r e a t e r t h e h i g h e r t h e r a t e o f i n f l a t i o n .
The
analysis
also
attempts to account
for the influence o f mortgage
a v a i l a b i l i t y o n house prices. I n s t i t u t i o n a l lenders, p r i n c i p a l l y b u i l d i n g societies,
t e n d t o change t h e i r interest rates r e l a t i v e l y i n f r e q u e n t l y w i t h t h e consequence
t h a t t h e d i f f e r e n t i a l b e t w e e n c a p i t a l a n d m o r t g a g e m a r k e t rates m a y v a r y
e s p e c i a l l y w h e n t h e f o r m e r are r i s i n g . F a i l u r e t o o f f e r " c o m p e t i t i v e " r a t e s
t o d e p o s i t o r s m a y l e a d t o a d e c l i n e i n m o r t g a g e s u p p l y a n d t h e use o f n o n p r i c e r a t i o n i n g b y lenders, w i t h the consequence t h a t house b u y e r s m a y be
c o n s t r a i n e d w i t h respect t o mortgage a v a i l a b i l i t y .
1
Section I I o f the paper details the manner i n w h i c h i n f l a t i o n , the tax
system and the mortgage i n s t r u m e n t m a y affect housing d e m a n d . Section I I I
d e v e l o p s a m o d e l t o e x p l a i n t h e r a t e o f change o f r e a l h o u s e p r i c e s a n d
1. A competitive market is taken to be one in which the mortgage rate adjusts to equate aggregate
mortgage demand and supply.
presents estimates using q u a r t e r l y I r i s h data over the p e r i o d 1 9 7 1 ( 3 ) t o
1980(4). The paper concludes that inflation w h e n acting i n concert w i t h the
t a x s y s t e m a n d t h e s t a n d a r d m o r t g a g e has s i g n i f i c a n t i m p l i c a t i o n s f o r h o u s i n g
d e m a n d and f o r real house prices.
II
Recent
INFLATION A N D HOUSING DEMAND
r e s e a r c h o n t h e h o u s i n g m a r k e t has suggested t h a t i n f l a t i o n m a y
h a v e t h r e e d i s t i n c t e f f e c t s o n t h e d e m a n d f o r h o u s i n g services. F i r s t , g i v e n
t h a t m o r t g a g e i n t e r e s t is t a x d e d u c t i b l e w h i l e c a p i t a l gains are n o t , i n f l a t i o n
r e d u c e s t h e a f t e r - t a x user cost o f h o u s i n g c a p i t a l a n d t h e r e f o r e
stimulates
housing d e m a n d . Second, via its i m p a c t o n the real value o f i n i t i a l repayments,
i n f l a t i o n m a y i n c r e a s e t h e r e a l cost o f c a p i t a l as p e r c e i v e d b y o w n e r - o c c u p i e r s
and consequently
r e d u c e s d e s i r e d c o n s u m p t i o n o f h o u s i n g services. T h i r d ,
as t h e n o m i n a l i n t e r e s t r a t e rises w i t h i n f l a t i o n t h e r e a l v a l u e o f t h e
of repayments
stream
necessary t o a m o r t i s e a m o r t g a g e d e c l i n e s m o r e r a p i d l y a n d
increases h o u s i n g d e m a n d .
( i ) The User
Cost of
Housing
I n a w o r l d o f a n t i c i p a t e d i n f l a t i o n t h e user cost p e r u n i t o f h o u s i n g c a p i t a l
m a y , f o r p u r p o s e s o f e x p o s i t i o n , be r e p r e s e n t e d b y
U C = (1 - x)(r + a i ) - hp,
(1)
w h e r e U C is t h e cost o f a u n i t o f t h e o w n e r o c c u p i e d h o u s i n g s t o c k , x is t h e
household's
m a r g i n a l t a x r a t e , r is t h e r e a l r a t e o f i n t e r e s t , a i is a n t i c i p a t e d
i n f l a t i o n a n d h p is t h e a n t i c i p a t e d r a t e o f c h a n g e o f h o u s e p r i c e s . I f i n f l a t i o n
is c o r r e c t l y a n t i c i p a t e d a n d r e l a t i v e p r i c e s are c o n s t a n t ( a i = h p ) t h e n , g i v e n a
c o n s t a n t r e a l r a t e o f i n t e r e s t , t h e e f f e c t o f a rise i n a i o n U C is d U C / d a i =
- x < 0 . T h a t i s , a rise i n a n t i c i p a t e d i n f l a t i o n r e d u c e s t h e user c o s t b y t h e
e x t e n t o f t h e h o u s e h o l d ' s m a r g i n a l t a x r a t e . I f t h e r e a l r a t e o f i n t e r e s t is n o t
i n d e p e n d e n t o f a n t i c i p a t e d i n f l a t i o n t h e e f f e c t o f a c h a n g e i n a i o n user c o s t
( a s s u m i n g ai = h p ) is d U C / d a i = ( 1 - x ) d r / d a i - x , w h e r e d r / d a i a p p r o x i m a t e s
t h e e x t e n t t o w h i c h t h e r e a l r a t e d e c l i n e s ( n o m i n a l r a t e does n o t rise) w i t h
an increase i n a n t i c i p a t e d i n f l a t i o n .
(ii)
The Mortgage
2
Instrument
A r e l a t i o n s h i p s u c h as ( 1 ) m a y n o t f u l l y d e s c r i b e t h e c o s t o f c a p i t a l as per­
ceived b y owner-occupiers.
T h i s p o s s i b i l i t y arises because o f t h e t y p e o f
m o r t g a g e i n s t r u m e n t t y p i c a l l y used t o f i n a n c e h o u s e p u r c h a s e . U n d e r
the
2. Define the nominal rate as i = r + ai so that U C = (1 - x)i - hp. Then dUC/dai = (1 - x)di/dai - 1.
If, for example, di/dai = 0 then dUC/dai = 1 .
-
standard mortgage instrument the annual repayment o f capital and interest
p e r p o u n d b o r r o w e d ( Q ) is g i v e n b y
Q = MR/[1
N
- (1 + M R ) ~ ] ,
(2)
w h e r e M R is t h e n o m i n a l m o r t g a g e r a t e a n d N is t h e a m o r t i s a t i o n p e r i o d o f
t h e i n i t i a l p r i n c i p a l . T o i l l u s t r a t e , c o n s i d e r a h o u s e h o l d w i t h a base y e a r
i n c o m e (year 0 ) o f £ 1 0 , 0 0 0 w h i c h wishes t o c o n t r a c t a mortgage equal t o
t w i c e i t s e x p e c t e d y e a r 1 i n c o m e . I f w e assume t h a t a l l n o m i n a l v a r i a b l e s
rise i n l i n e w i t h i n f l a t i o n a n d t h a t t h e r e a l r a t e o f i n t e r e s t is 3 p e r c e n t t h e n a
5 per cent i n f l a t i o n rate w o u l d i m p l y a year 1 i n c o m e o f £ 1 0 , 5 0 0 , a mortgage
o f £ 2 1 , 0 0 0 a n d a m o r t g a g e r a t e o f 8 p e r c e n t . I n t h i s case a n n u a l gross r e p a y ­
ments w o u l d be £ 1 , 9 6 7 o r 18.73 per cent o f year 1 i n c o m e . A l t e r n a t i v e l y , an
i n f l a t i o n r a t e o f 1 0 p e r c e n t w o u l d give r e p a y m e n t s o f £ 3 , 0 0 1 o r 2 7 . 2 8 p e r
cent o f year 1 i n c o m e . T h e real value o f i n i t i a l repayments w o u l d , therefore,
rise b y 4 6 p e r c e n t f r o m £ 1 , 8 7 3 at 5 p e r c e n t i n f l a t i o n t o £ 2 , 7 2 8 at 1 0 p e r
c e n t i n f l a t i o n e v e n t h o u g h t h e r e a l r a t e o f i n t e r e s t is c o n s t a n t .
The
third
effect
mentioned
a b o v e arises because i n f l a t i o n , w h i l e
not
affecting the real cost o f the mortgage w h e n c o m p u t e d over the a m o r t i s a t i o n
p e r i o d , a l t e r s t h e p r o f i l e o f t h e r e a l r e p a y m e n t s t r e a m . T h a t is, f o r a n y g i v e n
m o r t g a g e t h e p r e s e n t v a l u e o f t h e r e a l r e p a y m e n t s t r e a m necessary f o r f u l l
a m o r t i s a t i o n is t h e same w h e n d i s c o u n t e d at a c o n s t a n t r e a l r a t e o f i n t e r e s t
i r r e s p e c t i v e o f t h e n o m i n a l r a t e a p p l i e d . R a t h e r , t h e e f f e c t o f i n f l a t i o n is t o
" t i l t " t h e s t r e a m o f r e a l r e p a y m e n t s so t h a t t h e i r v a l u e d e c l i n e s m o r e r a p i d l y
t h e g r e a t e r is a n t i c i p a t e d i n f l a t i o n a t a n y g i v e n r e a l r a t e o f i n t e r e s t . T h e r e a s o n
for
t h i s t i l t is t h a t t h e m o r t g a g e i n s t r u m e n t r e q u i r e s t h e b o r r o w e r t o c o m ­
p e n s a t e t h e l e n d e r t o d a y f o r i n f l a t i o n w h i c h is e x p e c t e d t o o c c u r i n t h e f u t u r e
or,
as K e a r l suggests, " . . . t h e e x p e c t a t i o n o f i n f l a t i o n does n o t cause t h e
household's
r e a l f i n a n c i a l p o s i t i o n t o d e t e r i o r a t e , y e t i t has i n c r e a s e d
b u r d e n o f d e b t service since i t is o n l y i n t h e future
the
that inflation m a y deliver
h i g h e r n o m i n a l i n c o m e s w i t h w h i c h t o m a k e t h e current
(and future) inflation-
induced higher p a y m e n t s " ( 1 9 7 9 , p p . 1,115-1,116).
K e a r l a p p r o x i m a t e s t h i s t i l t i n g e f f e c t b y t h e e l a s t i c i t y o f t h e p r e s e n t value,
o f a given stream o f p a y m e n t s w i t h respect t o t h e d i s c o u n t rate d = 1/(1 + MR)..
T h e p r e s e n t v a l u e ( P V ) o f t h e r e p a y m e n t s s t r e a m is
N
(3)
w h e r e R E P is t h e a n n u a l gross r e p a y m e n t a n d t is t i m e . T h e e l a s t i c i t y o f P V
w i t h r e s p e c t t o d is
N
N
1
T = 2 t . d / 2 d.
1
l
T o e x p l a i n t h e r e l e v a n c e o f T , i t is u s e f u l t o v i e w a n i n d i v i d u a l ' s m o r t g a g e
d e m a n d as a d e c i s i o n t o a l l o c a t e p a r t o f h i s gross i n c o m e t o m o r t g a g e r e p a y ­
ments. T h e present value o f " d e s i r e d " repayments m u s t t h e n equal " d e s i r e d "
m o r t g a g e size, w h e n d i s c o u n t e d a t t h e c u r r e n t m o r t g a g e r a t e , a n d t h e h i g h e r
the interest rate the l o w e r the affordable mortgage given a p r i o r decision o n
R E P . T is t h e r e f o r e e q u i v a l e n t t o t h e e l a s t i c i t y o f m o r t g a g e d e m a n d w i t h
r e s p e c t t o t h e d i s c o u n t r a t e . A r e l a t i v e l y large v a l u e f o r T i m p l i e s t h a t a rise
i n t h e m o r t g a g e r a t e w i l l i n d u c e a r e l a t i v e l y large d e c l i n e i n m o r t g a g e size t o
offset the i m p a c t o f a h i g h interest rate o n R E P . Hence, given a positive
r e l a t i o n s h i p b e t w e e n h o u s i n g d e m a n d a n d m o r t g a g e size w e w o u l d ,
paribus,
expect
a negative
relationship between
T and the
ceteris
demand
for
h o u s i n g services.
H o w e v e r , w h e r e a s Q is p o s i t i v e l y r e l a t e d t o t h e m o r t g a g e r a t e , T d e c l i n e s
as M R rises. I t f o l l o w s t h a t a rise i n M R p r o d u c e s c o n f l i c t i n g e f f e c t s o n t h e
"perceived"
cost
housing demand
o f housing. First, b y increasing i n i t i a l repayments
is d e p r e s s e d . S e c o n d ,
(Q)
a rise i n M R r e d u c e s T a n d c o n ­
s e q u e n t l y s t i m u l a t e s h o u s i n g d e m a n d . I n o t h e r w o r d s , at a g i v e n r e a l r a t e o f
i n t e r e s t , a rise i n a n t i c i p a t e d i n f l a t i o n w h i c h is r e f l e c t e d i n n o m i n a l i n t e r e s t
r a t e s i n t e n s i f i e s t h e r e a l b u r d e n o f c u r r e n t r e p a y m e n t s b u t leads t o a m o r e
rapid decline i n future repayments relative t o income.
Ill
A M O D E L OF H O U S E PRICES
T h e m o d e l d e v e l o p e d i n t h i s s e c t i o n assumes t h a t t h e r a t e o f c h a n g e o f
r e a l h o u s e p r i c e s is p o s i t i v e l y r e l a t e d t o t h e excess d e m a n d f o r h o u s i n g
services, i . e . ,
(PH/P) /(PH/P) _
t
t
1
= (Hs^/Hs^ )
R
k > 0,
(5)
w h e r e P H is t h e p r i c e o f h o u s e s , P is a g e n e r a l i s e d p r i c e i n d e x , H s is t h e f l o w
o f h o u s i n g services a n d H s d is t h e d e m a n d f o r h o u s i n g services. K e a r l ( 1 9 7 9 )
a n d B u c k l e y ( 1 9 8 2 ) , a l o n g w i t h o t h e r s , assume t h a t H s is p r o p o r t i o n a l t o t h e
p h y s i c a l s t o c k o f o w n e r - o c c u p i e d h o u s i n g a n d , g i v e n t h a t n e t a d d i t i o n s are
s m a l l r e l a t i v e t o t h e s t o c k , t h e service f l o w c a n be t a k e n as f i x e d a t e a c h p o i n t
i n t i m e . A l t h o u g h t h i s i d e a is m a i n t a i n e d i n t h e p r e s e n t p a p e r , i t is m o d i f i e d
t o a c c o u n t f o r t h e f u r t h e r a s s u m p t i o n t h a t o w n e r - o c c u p i e r s are c o n c e r n e d
w i t h t h e m a r k e t v a l u a t i o n o f t h e q u a n t i t y o f services y i e l d e d b y t h e p h y s i c a l
s t o c k . I f q is t h e p h y s i c a l q u a n t i t y o f services d e r i v e d f r o m a g i v e n s t o c k ,
t h e n q . P H / P is a s s u m e d t o b e a m e a s u r e o f t h e r e a l v a l u e o f , o r r e a l e x p e n ­
d i t u r e o n , t h e g i v e n f l o w so t h a t H s is r e l a t e d t o t h e r e a l v a l u e o f t h e h o u s i n g
s t o c k R H K = H K . P H / P , w h e r e H K is t h e p h y s i c a l s t o c k . A s s u m i n g t h a t t h e
p h y s i c a l d e m a n d is u n i t elastic w i t h r e s p e c t t o P H / P , t h e n H s d c a n b e i n t e r -
p r e t e d as d e s i r e d r e a l e x p e n d i t u r e o n h o u s i n g s e r v i c e s .
3
I f the demand for
h o u s i n g services is d e t e r m i n e d b y s o m e v e c t o r o f e x o g e n e o u s v a r i a b l e s Z ,
t h e n ( 5 ) gives t h e f o l l o w i n g e q u i l i b r i u m r e l a t i o n s h i p f o r r e a l h o u s e p r i c e s :
Ln(PH/P)
t
= Ln[D(Z)] - LnHK .
t
(6)
T h e d e m a n d f o r h o u s i n g services is m o d e l l e d as
Hsd = D ( U C , R Q , T , A , Y , D F ) ,
(7)
w h e r e U C a n d T are d e f i n e d as a b o v e , R Q ( = Q / P ) is t h e r e a l v a l u e o f gross
repayments
per
unit
o f p r i n c i p a l b o r r o w e d , A is a m e a s u r e o f m o r t g a g e
a v a i l a b i l i t y , Y is r e a l i n c o m e a n d D F r e p r e s e n t s d e m o g r a p h i c f a c t o r s . T h e
user c o s t p e r u n i t o f h o u s i n g c a p i t a l is a p p r o x i m a t e d b y
UC = M R ( 1 - x ) ( l - V ) + A R ( 1 - x ) V - SUB - D P H ,
(ci)
w h e r e V is e q u i t y i n h o u s i n g , A R is t h e r e p r e s e n t a t i v e i n t e r e s t r a t e o n n o n h o u s i n g assets, S U B r e p r e s e n t s subsidies t o o w n e r - o c c u p i e r s a n d D P H is t h e
r a t e o f c h a n g e o f P H . T h e v a r i a b l e s V a n d S U B are m e a s u r e d as a p r o p o r t i o n
o f h o u s e v a l u e . T h e f i r s t t e r m i n ( 8 ) measures t h e a f t e r - t a x c o s t o f m o r t g a g e
finance
w h i l e the
second
approximates
t h e o p p o r t u n i t y cost o f h o l d i n g
w e a l t h i n h o u s i n g e q u i t y . T h e m e t h o d s used t o a p p r o x i m a t e x , S U B a n d the
o t h e r v a r i a b l e s are d e s c r i b e d i n t h e a p p e n d i x .
4
I f , for simplicity, M R and
A R are a s s u m e d t o b e e q u a l , t h e n U C is i n d e p e n d e n t o f V , a n d h e n c e
UC = M R ( 1 - x) - SUB - D P H .
(9)
M o r t g a g e a v a i l a b i l i t y is i n c l u d e d i n ( 7 ) o n t h e h y p o t h e s i s t h a t l e n d i n g
i n s t i t u t i o n s f r e q u e n t l y a l l o w t h e i r i n t e r e s t r a t e s t r u c t u r e t o get o u t o f l i n e
w i t h c a p i t a l m a r k e t rates w i t h t h e consequence t h a t funds available f o r l e n d ­
i n g m a y f a l l b e l o w t h e l e v e l w h i c h w o u l d be o f f e r e d i n a m o r e " c o m p e t i t i v e "
market
structure.
stitutions resort
5
W h e n f a c e d w i t h a n excess d e m a n d f o r m o r t g a g e s , i n ­
t o n o n - p r i c e r a t i o n i n g as a m e a n s o f a l l o c a t i n g a v a i l a b l e
s u p p l y . This t y p e o f behaviour m a y mean t h a t b o r r o w e r s can o b t a i n relatively
c h e a p f i n a n c e b u t t h e y m a y n o t get a l l - t h e y desire so t h a t t h e i r h o u s i n g
3. Partial support for this assumption may be found in Kenneally and McCarthy (1982). Unfor­
tunately the comparison is not completely valid as these authors use H K as the dependent variable
in their demand function.
4. The cost of capital proxy is deficient in at least two respects. First, no account is taken of property
taxes (rates). However, it should be noted that rates remission was available on new houses for most of.
the sample period and rates were abolished in 1977. Second, the expected rate of change of PH i;i
proxied by the actual rate. This assumption is made for computational simplicity. However, in the
regression results reported below, U C is measured as a four quarter moving average. See equation (11).
5. Assuming that mortgage supply is a positive function of MR. For evidence of this see Hewitt and
Thorn (1979) and O'Loughlin (1980).
decisions
may
be
constrained
mortgage
availability
b y mortgage availability. T h e measure o f
4
( A ) is p r o x i e d b y D S K / . 2 5 2 D S K _
{
t
, where D S K
;
is t h e g r o w t h r a t e o f t h e r e a l s t o c k ( d e f l a t e d b y P H ) o f b u i l d i n g s o c i e t y share
a n d d e p o s i t l i a b i l i t i e s . D S K is u s e d o n t h e a s s u m p t i o n t h a t m o r t g a g e l e n d i n g
is c l o s e l y r e l a t e d t o t h e f l o w o f savings t h r o u g h i n s t i t u t i o n s . T h e s p e c i f i c a t i o n
t h e r e f o r e assumes t h a t m o r t g a g e r a t i o n i n g w i l l b e i n t e n s i f i e d ( r e l a x e d ) i f t h e
c u r r e n t g r o w t h o f shares a n d d e p o s i t s falls (rises) r e l a t i v e t o t h e g r o w t h r a t e
o v e r t h e p r e v i o u s f o u r q u a r t e r s . A l t e r n a t i v e p r o x i e s s u c h as t h e average l o a n
t o v a l u e r a t i o a n d t o t a l m o r t g a g e a p p r o v a l s w e r e also t e s t e d b u t t h e s p e c i f i ­
6
cations p r o v e d " i n f e r i o r " o n the usual statistical c r i t e r i o n .
As Irish data do
n o t i n c l u d e a n o f f i c i a l series o n r e a l d i s p o s a b l e i n c o m e , t h e i n d e x o f i n d u s t r i a l
production
i n transportable
goods industries was used
as a p r o x y .
This
v a r i a b l e gave b e t t e r r e s u l t s t h a n o t h e r p r o x i e s s u c h as a n e a r n i n g s i n d e x .
D F was p r o x i e d b y t h e r a t i o o f marriages t o p r i v a t e sector c o m p l e t i o n s . Once
again t h e p a u c i t y o f o f f i c i a l data necessitated such a p r o x y . F i n a l l y , t h e real
p r i c e o f h o u s i n g was m e a s u r e d
b y t h e r a t i o o f t h e average p r i c e o f n e w
houses, f o r w h i c h mortgages were a p p r o v e d b y the m a i n l e n d i n g i n s t i t u t i o n s ,
t o t h e consumer price i n d e x . I n o r d e r t o c o n t r o l f o r q u a l i t y changes, t h e
n o m i n a l p r i c e o f h o u s e s w a s d e f l a t e d b y t h e average f l o o r area ( i n s q u a r e
m e t r e s ) o f houses f o r w h i c h p l a n n i n g p e r m i s s i o n has b e e n g r a n t e d . A s t h e r e
is a n o b v i o u s d e l a y b e t w e e n g r a n t i n g p l a n n i n g p e r m i s s i o n a n d c o m p l e t i o n ,
t h e d e f l a t o r w a s l a g g e d b y six q u a r t e r s .
7
A s s u m i n g a log-linear specification
f o r ( 7 ) a n d s u b s t i t u t i n g i n t o ( 5 ) gives
ALn(PH/P)
= ka
t
Q
+ kajUC
ka LnY
5
{
t
+ ka LnRQ + ka LnT
2
+ ka LnDF
6
t
t
3
- kLnRHK^
t
+ ka LnA
4
{
+ u ,
{
+
(10)
w h e r e A is t h e f i r s t d i f f e r e n c e o p e r a t o r a n d u is a r a n d o m d i s t u r b a n c e t e r m
w i t h c o n s t a n t v a r i a n c e a n d E ( u ) = 0 . T h e e x p e c t e d signs o f t h e c o e f f i c i e n t s
i n ( 1 0 ) are, a j , a , a
2
3
< 0 and a ,a ,a ,k > 0.
4
5
g
A s user c o s t is m e a s u r e d as a p e r c e n t a g e
rate the specification o f (10)
p e r m i t s a variable elasticity o f h o u s i n g d e m a n d w i t h respect t o U C . T o a l l o w
for
t h e p o s s i b i l i t y t h a t t h e i m p a c t o n h o u s i n g d e m a n d o f changes i n t h e
d e t e r m i n i n g variables m a y be
spread
o v e r several p e r i o d s a f o u r
quarter
6. The growth of deposits at thrift institutions has been used as an availability proxy in several housing
sector studies. See Jaffee and Rosen (1979).
7. It would be more satisfactory to use a house price series which reflected existing, as well as new,
house prices. A sufficiently long quarterly series on second-hand house prices is, unfortunately, not
available.
8
K o y c k l a g s t r u c t u r e w a s i m p o s e d o n t h e R H S v a r i a b l e s o f ( 7 ) . T h i s l a g is
given b y
Zb.LnX^
where b
Q
= .2, b j = .3, b
=
g
.3, b
(11)
= .2 a n d X r e p r e s e n t s each o f t h e r i g h t
g
h a n d v a r i a b l e s i n ( 7 ) . E s t i m a t i n g ( 1 0 ) b y O L S o v e r 1 9 7 1 ( 3 ) t o 1 9 8 0 ( 4 ) gave
the following result:
ALn(PH/P)
= 2.676 - 2.37UC. - . 8 4 1 L n R Q
(2.99)
(6.30)
- 1.09LnT
+ .662LnA
(5.75)
(2.00)
(7.66)
+ 1.604LnY + .262LnDF - .953LnRHK
. + SEASONALS
t
(5.99)
R=.768
D W = 2.049
(2.37)
1
(8.16)
SEE = .037
( t - s t a t i s t i c s are i n p a r e n t h e s e s ) ,
w h i c h yields the f o l l o w i n g e q u i l i b r i u m relationship f o r real house prices
Ln(PH/P)
t
= 2.807 - 2 . 4 8 6 U C - . 8 8 2 L n R Q - 1 . 1 4 3 L n T
t
.694LnA
t
t
+ 1.683LnY + .274LnDF t
t
t
+
LnRHK .
t
O f t h e seven e s t i m a t e d c o e f f i c i e n t s i n ( 1 2 ) f i v e are s i g n i f i c a n t a t t h e 1 p e r
c e n t l e v e l a n d t h e o t h e r t w o ( o n L n A a n d L n D F ) are s i g n i f i c a n t at t h e 5 p e r
cent level. T h e value o f the D u r b i n - W a t s o n statistic together w i t h a critical
level
9
o f . 8 3 4 f o r t h e B o x - P i e r c e Q - s t a t i s t i c suggests t h a t s e r i a l c o r r e l a t i o n is
n o t a p r o b l e m , w h i l e t h e e s t i m a t e d c o e f f i c i e n t o f d e t e r m i n a t i o n is r e a s o n a b l e
g i v e n t h a t t h e d e p e n d e n t v a r i a b l e is f i r s t d i f f e r e n c e d .
T h e r e s u l t s c o n f i r m t h a t b o t h user c o s t a n d t h e d i s t o r t i o n s d u e t o i n i t i a l
p a y m e n t s ( R Q ) a n d t i l t i n g ( T ) are, along w i t h mortgage a v a i l a b i l i t y , signifi­
cant determinants o f real house prices and housing d e m a n d . T h e estimate for
k = . 9 5 3 i m p l i e s t h a t t h e r e a l v a l u e o f t h e service f l o w adjusts r a p i d l y t o
d e m a n d p r e s s u r e . F o r e x a m p l e , a 1 p e r c e n t rise i n Y m e a n s t h a t t h e e q u i ­
l i b r i u m l e v e l o f t h e r e a l p r i c e m u s t increase b y 1.683 p e r c e n t f o r t h e g i v e n
s t o c k t o b e w i l l i n g l y h e l d , i . e . , t h e r e a l v a l u e o f t h e service f l o w m u s t increase
b y this a m o u n t t o restore e q u a l i t y b e t w e e n H s d and Hs. A l l o w i n g for the
i m p o s e d K o y c k l a g P H / P rises b y . 3 2 0 8 p e r c e n t i n t h e c u r r e n t q u a r t e r a n d
t h e f u l l a d j u s t m e n t is c o m p l e t e d w i t h i n t w o y e a r s .
T h e p o s i t i v e sign o f t h e i n c o m e e l a s t i c i t y i n d i c a t e s t h a t h o u s i n g is a n o r m a l
8. Alternatively the moving average -terms may be regarded as proxing the expected values of the
R H S variables in (7). The model then combines the partial adjustment mechanism (5) and adap­
tive expectations (11) with the distributed lags imposed rather than being subjected to a Koyck
transformation.
9. The critical level is the significance level at which the null hypothesis of no serial correlation in
just rejected.
/
HOUSE PRICES AND INFLATION
T a b l e 1 : Interest
MR
Q
(1)
(2)
rate
elasticities
T
E
(3)
r
(4)
(5)
£
%Ch.
P H / P
(7)
(6)
.04
.0640
10.9930
.44
-.17
-.246
-6.150
.06
.0782
10.0720
.59
-.25
-.316
-5.267
.08
.0936
9.2250
.70
-.33
-.352
-4.400
.10
.1101
8.4580
.79
-.41
-.371
-3.710
.12
.1275
7.7708
.84
-.47
-.379
-3.158
.14
.1454
7.1610
.89
-.52
-.397
-2.835
.16
.1640
6.6230
.92
-.57
-.399
-2.493
g o o d . I t s s t a t i s t i c a l s i g n i f i c a n c e is i n c o n t r a s t w i t h t h e r e s u l t r e p o r t e d b y
K e n n e a l l y a n d M c C a r t h y ( 1 9 8 2 ) w h o also use a d i f f e r e n t p r o x y .
Assuming a constant real rate o f interest the i m p a c t o f i n f l a t i o n o n house
p r i c e s c a n be a p p r o x i m a t e d b y t h e e l a s t i c i t y o f P H / P w i t h r e s p e c t t o t h e
mortgage rate. F r o m (13)
E
where E
p H
p
H
/
^ , E Q ,E
p
p
t
= a j M R ( l - x) + a E
2
Q
+a E
3
T
,
(14)
are t h e e l a s t i c i t i e s o f P H / P , Q a n d T w i t h r e s p e c t t o
M R . Table 1 presents estimates
o f these e l a s t i c i t i e s f o r d i f f e r e n t values o f
M R a s s u m i n g a m a r g i n a l t a x r a t e o f 3 5 p e r c e n t . C o l u m n s ( 2 ) a n d ( 3 ) give
estimates
o f Q a n d T w h i l e C o l u m n s ( 4 ) a n d ( 5 ) give t h e
e l a s t i c i t i e s . C o l u m n ( 6 ) gives E
p
H
/
p
corresponding
and C o l u m n (7) shows the percentage
change i n real price associated w i t h a 1 per cent change i n M R , i.e., f r o m .04
t o .05. A l t h o u g h the absolute value o f E p /
H
P
increases w i t h M R i t d o e s so a t a
d i m i n i s h i n g r a t e . H e n c e , t h e i m p a c t o f a 1 p e r c e n t rise i n t h e m o r t g a g e r a t e ,
Column
( 7 ) , d i m i n i s h e s as M R rises. T h i s p h e n o m e n o n
is c a u s e d b y
the
i n f l u e n c e o f t h e t i l t i n g e f f e c t as p r o x i e d b y T . A s M R rises t h e e f f e c t o n Q
a l o n g w i t h i n c r e a s e d user c o s t r e d u c e s b o t h h o u s i n g d e m a n d a n d r e a l p r i c e .
H o w e v e r , as t h e c u r r e n t l e v e l o f r e p a y m e n t s
the
future
stream
declines
more
rapidly
rise w i t h Q , t h e r e a l v a l u e o f
as i n d i c a t e d b y t h e
increasing
absolute value o f the interest elasticity o f T . T h e i m p a c t o f higher current
n o m i n a l , a n d r e a l , r e p a y m e n t s is t h e r e f o r e m o d e r a t e d b y t h e s t i m u l u s t o
d e m a n d t h r o u g h an e x p e c t e d decline i n t h e real value o f the f i x e d r e p a y m e n t .
IV CONCLUSIONS
A n i m p o r t a n t i m p l i c a t i o n o f t h e r e s u l t s r e p o r t e d i n S e c t i o n I I I is t h a t t h e
s t a n d a r d m o r t g a g e w h i c h f i x e s a n n u a l p a y m e n t s i n n o m i n a l t e r m s has a dis­
t o r t i n g effect o n housing d e m a n d d u r i n g i n f l a t i o n a r y periods. Even i f the
u s e r c o s t o f c a p i t a l is u n a f f e c t e d b y i n f l a t i o n t h e d e m a n d f o r h o u s i n g m a y
still
be
hold's
influenced b y the manner
perception
view the most
in which
o f h o u s i n g costs.
inflation
affects
the
F r o m the owner-occupier's
house­
point of
i m p o r t a n t i n f l a t i o n - i n d u c e d d i s t o r t i o n is l i k e l y t o b e
the
e f f e c t o n i n i t i a l o r c u r r e n t r e p a y m e n t s . T h a t i s , a rise i n n o m i n a l i n t e r e s t
rates w i l l increase t h e real value o f r e p a y m e n t s
e v e n i f i n f l a t i o n is f u l l y
a n t i c i p a t e d . T h i s p h e n o m e n o n is s o m e t i m e s r e f e r r e d t o as f r o n t - e n d l o a d i n g ,
w h i c h m e a n s t h a t w h e n t h e m o r t g a g e r a t e rises, t h e n o m i n a l v a l u e o f t h e
r e p a y m e n t rises r e l a t i v e t o i n c o m e , even w h e n i n f l a t i o n is f u l l y a n t i c i p a t e d
a n d r e a l i n c o m e s are c o n s t a n t . T h e r e s u l t s , t h e r e f o r e , l e n d s u p p o r t t o t h e
introduction
o f alternative
mortgage
instruments
s u c h as t h e r e a l v a l u e
m o r t g a g e , discussed b y W h i t l e y ( 1 9 7 5 ) , w h i c h fixes r e p a y m e n t s i n r e a l r a t h e r
t h a n i n n o m i n a l terms. I n d e x i n g n o m i n a l repayments n o t o n l y eliminates the
f r o n t - e n d l o a d i n g p r o b l e m b u t also t h e t i l t i n g e f f e c t o f t h e f i x e d n o m i n a l
p a y m e n t system.
Further,
mortgage
given that
interest
mortgage
rate, the
s u p p l y is a n i n c r e a s i n g f u n c t i o n
of
the
s i g n i f i c a n c e o f t h e a v a i l a b i l i t y p r o x y suggests
that a more competitive market structure m i g h t benefit p o t e n t i a l entrants
such
as
n e w l y - m a r r i e d couples. Increased
competition might, of
course,
l e a d t o h i g h e r m o r t g a g e i n t e r e s t rates b u t t h e c o n s e q u e n t f i n a n c i n g p r o b l e m s
can be dealt w i t h b y o f f e r i n g alternative mortgage r e p a y m e n t systems.
The
r e a l a d v a n t a g e is t o b e f o u n d i n i n c r e a s e d m o r t g a g e a v a i l a b i l i t y f o r t h o s e w h o
are w i l l i n g t o p a y t h e c o m p e t i t i v e p r i c e . I n c r e a s e d a v a i l a b i l i t y w o u l d
necessarily
not
l e a d t o p e r m a n e n t l y h i g h e r p r i c e s as t h e r e a l p r i c e / a v a i l a b i l i t y
r e l a t i o n s h i p is a c o n s e q u e n c e o f a n o n - c o m p e t i t i v e m a r k e t s t r u c t u r e .
A s t h e m o d e l assumes t h a t b o t h t h e h o u s i n g s t o c k a n d n e t a d d i t i o n s t o
i t are g i v e n , t h e r e s u l t s m u s t b e t r e a t e d w i t h s o m e c a u t i o n . A m o r e c o m ­
prehensive
model would
attempt
t o e x p l a i n starts, c o m p l e t i o n s and
the
s u p p l y o f m o r t g a g e f i n a n c e i n a d d i t i o n t o r e a l h o u s e p r i c e s . H o w e v e r , i t is
reassuring
reflect
to
note
that
the
significance o f i n f l a t i o n - i n d u c e d d i s t o r t i o n s
the results r e p o r t e d b y K e a r l
(1979) and
U S A , and b y Buckley and Ermish (1982) for the U K .
Follain
(1982) for the
REFERENCES
B U C K L E Y , R . M . , 1 9 8 2 . " A S i m p l e T h e o r y of the U K H o u s i n g S e c t o r " , Urban
Studies,
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D A T A APPENDLX
4
A
Mortgage availability proxied b y D S K / . 2 5 S D S K _
£
C O M P Private sector c o m p l e t i o n s . ( Q B H S )
t
r
1
DF
R a t i o o f marriages t o C O M P . ( I S B )
HK
O w n e r - o c c u p i e d h o u s i n g s t o c k . C o m p u t e d b y u s i n g t h e 1 9 7 1 census
MR
Mortgage rate. (CB)
P
C P I , 1975 = 100. (ISB)
figure and C O M P assuming an annual depreciation rate o f 2 per cent.
PH
Average p r i c e o f n e w houses f o r w h i c h mortgage loans were a p p r o v e d
by
t h e m a i n l e n d i n g agencies d e f l a t e d b y F A _ ; w h e r e F A = average
t
g
f l o o r area o f h o u s e s f o r w h i c h p l a n n i n g p e r m i s s i o n has b e e n g r a n t e d .
(QBHS and ISB)
SK
S t o c k o f b u i l d i n g s o c i e t y share a n d d e p o s i t l i a b i l i t i e s d e f l a t e d b y P H .
SUB
Subsidies t o
(CB)
owner-occupiers.
T o t a l value o f grants and
subsidies d i v i d e d b y the n u m b e r
D e p a r t m e n t o f t h e E n v i r o n m e n t Annual
Y
mortgage
o f grants a n d subsidies a l l o c a t e d .
Report.
Index o f p r o d u c t i o n i n transportable goods industries, 1975 = 100.
(ISB)
x
Marginal tax rate estimated
as f o l l o w s : t h e Q B H S gives t h e
income
o f b o r r o w e r s c l a s s i f i e d b y i n c o m e class. T h e i n c o m e o f t h e " a v e r a g e "
b o r r o w e r was c o m p u t e d b y y = w l . M l + = . . . + w n . M n , w h e r e w i = t h e
proportion o f borrowers
i n i n c o m e class i a n d M i = t h e
mid-point
class i . A s t h e t o p a n d b o t t o m classes are o p e n - e n d e d t h e m i d - p o i n t s
where assumed t o be L i + / - £ 5 0 0 , L i + / -
= t h e class l i m i t . G i v e n t h i s
e s t i m a t e o f y , x was c o m p u t e d as t h e M T R a p p l i c a b l e t o a childless
m a r r i e d c o u p l e u s i n g t h e t a x b a n d s a n d r a t e s i n successive B u d g e t s .
CB
Central
ISB
Irish
QBHS
Quarterly
Bank
Quarterly
Statistical
Bulletin
Bulletin
Bulletin
of Housing
Statistics