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Regional model of multi family housing starts : an inventory adjustment approach 1984

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REGIONAL MODEL OF MULTI FAMILY HOUSING STARTS: AN INVENTORY ADJUSTMENT APPROACH by JUDY A. FOUNTAIN B.E.S., U n i v e r s i t y Of W a t e r l o o , 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) .in THE FACULTY OF GRADUATE STUDIES Commerce and B u s i n e s s A d m i n i s t r a t i o n ( U r b a n L a n d E c o n o m i c s ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d S t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA M a r c h 1984 © J u d y A. F o u n t a i n , 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an "advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the head o f my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s u n derstood t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Urban Land Economics The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 27 March (3/81) ABSTRACT The d e c l i n e i n m u l t i f a m i l y h o u s i n g s t a r t s i n U r b a n Canada d u r i n g t h e 1970's and t h e a t t e n d a n t low v a c a n c y r a t e s has g e n e r a t e d comment on t h e e f f i c i e n c y o f h o u s i n g m a r k e t s a nd t h e p o s s i b i t y o f a h o u s i n g c r i s i s . T r a d i t i o n a l l y , e x i s t i n g v a c a n t u n i t s a r e c i t e d as a b u f f e r between t h e demand and s u p p l y . T h i s p a p e r p r o p o s e s t h a t t h e i n v e n t o r y o f new u n i t s o f f e r s a more d i r e c t b u f f e r . T h e r e f o r e t h e use o f an i n v e n t o r y a d j u s t m e n t m o d el t o e s t i m a t e and p r e d i c t m u l t i f a m i l y h o u s i n g s t a r t s i s s u g g e s t e d . The t h e o r e t i c a l m o d el s u g g e s t s t h a t t h e r e i s some d e s i r e d i n v e n t o r y l e v e l w h i c h b u i l d e r s o r i n v e s t o r s w i l l t r y t o m a i n t a i n d e p e n d i n g on e x p e c t e d p r o f i t a b i l i t y , t h e r e l a t i v e y i e l d on o t h e r i n v e s t m e n t s a nd t h e c o s t o f m a i n t a i n i n g v a c a n t u n i t s . Demand f o r new r e n t a l u n i t s w i l l d e p e n d upon t h e d e o m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n , u n e m p l o y m e n t , i n c o m e , a nd t h e r e l a t i o n s h i p b e t ween r e n t s o w n e r s h i p c o s t s a n d t h e c o s t o f o t h e r g oods and s e r v i c e s . S t a r t s w i l l be s e t t o s a t i s f y t h e e x p e c t e d demand and a d j u s t a c t u a l i n v e n t o r y l e v e l s t o t h e d e s i r e d i n v e n t o r y l e v e l . Q u a r t e r l y d a t a f o r t h e V a n c o u v e r CMA, f r o m 1963 t o 1982 a r e u s e d t o t e s t t h i s m o d e l . The e m p i r i c a l a n a l y s i s c o n s i s t s of t h r e e p a r t s : a s t r u c t u r a l - m o d el b a s e d on t h e i n v e n t o r y a d j u s t m e n t p r o c e s s , a t i m e s e r i e s m o d e l t o p r o v i d e a measure f o r e v a l u a t i n g t h e s u c c e s s o f t h e s t r u c t u r a l m o d e l , and an a n a l y s i s o f t h e f o r e c a s t i n g c a p a b i l i t i e s o f t h e s e two m o d e l s . D a t a f r o m 1963 t o 1980 a r e u s e d t o e s t i m a t e t h e m o d e l s a n d 1981 t o 1982 d a t a a r e m a i n t a i n e d t o t e s t t h e f o r e c a s t s . The r e s u l t s s u f f e r f r o m i n a d e q u a c i e s o f t h e a v a i l a b l e d a t a , i m m e a s u r a b l e i m p a c t s o f g o v e r n m e n t p o l i c y a n d p r o g r a m s and p o s s i b l e i d i o s y n c r a c i e s o f t h e V a n c o u v e r h o u s i n g m a r k e t . I n g e n e r a l , t h e r e s u l t s i n d i c a t e t h a t i n v e n t o r i e s do p r o v i d e a b u f f e r b e t w e e n t h e demand and s u p p l y o f m u l t i f a m i l y h o u s i n g u n i t s . As s u c h , t h e v a c a n c y r a t e o f e x i s t i n g u n i t s , i n i s o l a t i o n , i s an i n s u f f i c i e n t i n d i c a t o r o f m a r k e t a c t i v i t y and r e s p o n s e . S i m i l a r a n a l y s i s f o r o t h e r u r b a n c e n t r e s i n Canada i s n e e d e d t o d e t e r m i n e t h e u n i q u e n e s s o f t h e s e r e s u l t s . A l s o , i t may be p o s s i b l e t o d e v e l o p an i m p r o v e d f o r e c a s t i n g model by i n c o r p o r a t i n g t h e t i m e s e r i e s c o e f f i c i e n t s w i t h t h e s t r u c t u r a l m o d e l . TABLE OF CONTENTS A b s t r a c t i i L i s t o f T a b l e s v L i s t o f F i g u r e s v i 1 . I n t r o d u c t i o n 1 2. L i t e r a t u r e R e v i e w .6 2. 1 H o u s i n g C y c l e s 7 2.2 S u p p l y o f H o u s i n g - E l a s t i c i t i e s 10 2.3 H o u s i n g S t a r t s M o d e l s . . . . 12 2.3.1 M a i s e l - I n v e n t o r y A d j u s m e n t M o d e l 14 2.3.2 S m i t h - B i - S e c t o r a l H o u s i n g M o d e l 16 .2.3.3 J a f f e e & R o s e n - C r e d i t A v a i l a b i l i t y & R e s i d e n t i a l C o n s t r u c t i o n 19 2.3.4 R o s e n - R e g i o n a l M o d e l o f M u l t i F a m i l y H o u s i n g S t a r t s 22 2.4 Comments on E x i s t i n g Work 23 3. I m p a c t s o f Government P r o g r a m s and P o l i c y 26 3.1 G e n e r a l P o l i c y C h a n g e s 26 3.2 Demand O r i e n t e d P o l i c i e s 27 3.3- S u p p l y O r i e n t e d P o l i c i e s 29 3.4 I m p a c t s on t h e M u l t i F a m i l y M a r k e t . . . . . 32 4. T h e o r e t i c a l M o d e l 37 4.1 I n v e n t o r y A d j u s t m e n t C o n c e p t . . . . . . . 38 4.2 M o d e l S p e c i f i c a t i o n 42 4.2.1 O v e r a l l M o d e l .43 4.2.2 Demand 46 4.2.3 S u p p l y 52 5. D a t a 56 5.2 M o d e l R e q u i r e m e n t s 56 5.2 P o p u l a t i o n and H o u s i n g 58 5.3 C P l I n d e x e s 61 5.4 S t a r t s / I n v e n t o r i e s 62 5.5 A p p l i c a t i o n t o t h e M o d e l ..76 6. E m p i r i c a l A n a l y s i s and T e s t i n g 80 6.1 E m p i r i c a l M o d e l a nd A n a l y s i s 80 6.2 E m p i r i c a l R e s u l t s 84 6.2.1 A b s o r p t i o n s 84 6.2.2 S t a r t s . .89 6.3 Time S e r i e s M o d e l 101 6.4 F o r e c a s t s and T e s t s o f M o d e l R e l i a b i l i t y 103 7. C o n c l u s i o n s a n d F u t u r e R e s e a r c h 113 N o t e s 117 i i i B i b l i o g r a p h y 120 A p p e n d i x A 125 A p p e n d i x B 128 A p p e n d i x C 138 i v L I S T OF TABLES 5.1 H o u s e h o l d s - V a n c o u v e r CMA.... 59 5.2 M a r k e t and Non M a r k e t H o u s i n g S t a r t s , V a n c o u v e r 1982 64 5.3 M a r k e t and Non M a r k e t H o u s i n g S t a r t s V a n c o u v e r 1982 65 5.4 S o c i a l H o u s i n g P o r j e c t A p p r o v a l s - V a n c o u v e r 67 5.5 R e g r e s s i o n f o r C o m p l e t i o n s w i t h S t a r t s 72 5.6 V a n c o u v e r V a c a n c y R a t e s 75 5.7 V a n c o u v e r H o u s i n g U n i t s D e m o l i t i o n P e r m i t s 77 6.1 V a r i a b l e L i s t f o r A b s o r p t i o n E q u a t i o n . 82 6.2 V a r i a b l e L i s t f o r S t a r t s E q u a t i o n 83 6.3 R e g r e s s i o n R e s u l t s - A b s o r p t i o n s . . . . 85 6.4 R e g r e s s i o n R e s u l t s - M u l t i F a m i l y H o u s i n g S t a r t s 1963-1980 91 6.5 R e g r e s s i o n R e s u l t s - M u l t i F a m i l y H o u s i n g S t a r t s 1963-1970 98 6.6 R e g r e s s i o n R e s u l t s - M u l t i F a m i l y H o u s i n g S t a r t s 1971-1980 99 6.7 R e g r e s s i o n R e s u l t s - M u l t i F a m i l y H o u s i n g S t a r t s I n c l u d i n g V a c a n c y R a t e s 102 6.8 Time S e r i e s M o d e l s 104 6.9 F o r e c a s t i n g R e s u l t s M e a s u r e s 107 v L I S T OF FIGURES 4.1 I n v e n t o r y A d j u s t m e n t P r o c e s s .....40 4.2 M o d e l S t r u c t u r e M u l t i F a m i l y H o u s i n g S t a r t s .....45 5.1 V a n c o u v e r Q u a r t e r l y M u l t i F a m i l y H o u s i n g S t a r t s 69 5.2 V a n c o u v e r Q u a r t e r l y M u l t i F a m i l y H o u s i n g C o m p l e t i o n s 70 5.3 V a n c o u v e r Q u a r t e r l y M u l t i F a m i l y H o u s i n g I n v e n t o r y -. 73 5.4 V a n c o u v e r Q u a r t e r l y M u l t i F a m i l y H o u s i n g A b s o r p t i o n s 74 5.5 V a n c o u v e r I n v e n t o r y A d j u s t m e n t 79 6.1 R e s i d u a l A n a l y s i s f o r E q u a t i o n 3 .95 6.2 R e s i d u a l A n a l y s i s f o r E q u a t i o n 5 96 6.3 P r e d i c t e d M u l t i F a m i l y H o u s i n g S t a r t s M o d e l 2 109 6.4 P r e d i c t e d M u l t i F a m i l y H o u s i n g S t a r t s - M o d e l 4 110 6.5 P r e d i c t e d M u l t i F a m i l y H o u s i n g S t a r t s - M o d e l 5 111 v i ACKNOWLEDGEMENT The a u t h o r i s i n d e b t e d t o D e n n i s C a p o z z a and Tae Oum f o r t h e u s e f u l comments and s u g g e s t i o n s . S p e c i a l t h a n k s i s e x t e n d e d G e o r g e Gau f o r h i s i n v a l u a b l e a s s i s t a n c e and e n c o u r a g e m e n t F i n a n c i a l a s s i s t a n c e was p r o v i d e d by t h e Canada M o r t g a g e and H o u s i n g C o r p o r a t i o n . v i i 1 1 . INTRODUCTION The e x t r e m e v o l a t i l i t y o f r e s i d e n t i a l c o n s t r u c t i o n h a s a t t r a c t e d e x t e n s i v e r e s e a r c h a n d comment. O v e r t h e l a s t two d e c a d e s , i n C a n a d a , t o t a l a n n u a l r e s i d e n t i a l u n i t s t a r t s i n c r e a s e d f r o m 130,095 i n 1962, t o a peak i n 1976 o f 273,203 u n i t s a n d d r o p p e d t o a low o f 125,860 u n i t s i n 1982. S i m i l a r e x t r e m e p a t t e r n s c a n be n o t e d i n most C a n a d i a n u r b a n c e n t r e s w i t h r e s i d e n t i a l c o n s t r u c t i o n a c t i v i t y p e a k i n g i n t h e m i d 1 9 7 0 ' s . To a i d i n e c o n o m i c a n a l y s i s , f o r e c a s t i n g , g o v e r n m e n t p o l i c y e v a l u a t i o n and i m p l e m e n t a t i o n , r e s e a r c h h a s been u n d e r t a k e n t o e x p l a i n t h i s v o l a t i l i t y i n c o n s t r u c t i o n and t h e s t r u c t u r e of h o u s i n g m a r k e t s . T r a d i t i o n a l l y , v a c a n c y r a t e s have been c i t e d a s l i n k i n g t h e demand and s u p p l y c o m p o n e n t s of t h e h o u s i n g m a r k e t . T h i s p a p e r a t t e m p t s t o e x a m i n e t h e r o l e o f i n v e n t o r y o f new u n i t s a s a more d i r e c t b u f f e r b e t w e e n t h e demand and s u p p l y o f u n i t s i n t h e h o u s i n g m a r k e t . I n v e s t i g a t i o n o f t h e i m p o r t a n c e o f i n v e n t o r y l e v e l s i n t h e d e t e r m i n a t i o n o f h o u s i n g p r o d u c t i o n w i l l e n h a n c e f o r e c a s t s o f f u t u r e r e s i d e n t i a l c o n s t r u c t i o n a c t i v i t y , u n d e r s t a n d i n g o f t h e u n d e r l y i n g m a r k e t f o r c e s , and t h e i m p a c t o f e x i s t i n g m a r k e t c o n d i t i o n s a n d d e m o g r a p h i c t r e n d s on t h e h o u s i n g m a r k e t . D e s p i t e t h e o b v i o u s c y c l i c a l n a t u r e o f t o t a l r e s i d e n t i a l c o n s t r u c t i o n , d i s t i n c t t r e n d s i n t h e m u l t i f a m i l y a n d s i n g l e f a m i l y m a r k e t s s u g g e s t s t h e n e e d t o e x a m i n e t h e s e two m a r k e t s e c t o r s s e p a r a t e l y . M u l t i f a m i l y s t a r t s i n Canada p e a k e d i n 1969 a t 104,622 u n i t s , a n d t h e n , a f t e r a r e l a t i v e l y s t a b l e 2 p e r i o d , d r o p p e d d r a m a t i c a l l y f r o m 1973 t o 1974 ( 9 8 , 7 7 6 u n i t s t o 67,599 u n i t s ) . S i n c e 1974, m u l t i f a m i l y s t a r t s h a v e b e e n d e c l i n i n g w i t h e x t r e m e l o w s n o t e d i n 1977 a n d e v e n f u r t h e r d e c l i n e s by 1982. S i n g l e f a m i l y c o n s t r u c t i o n a l s o p e a k e d i n 1973 a t 85,089 u n i t s b u t d i d n o t d e c l i n e a s s i g n i f i c a n t l y i n 1974. M u l t i f a m i l y c o n s t r u c t i o n i s s t i l l a t a b o u t 50 p e r c e n t o f t h e p r e - 1 9 7 3 l e v e l s o f c o n s t r u c t i o n . T h i s r e i n f o r c e s t h e b e l i e f t h a t t h e two m a r k e t s r e s p o n d t o d i f f e r e n t s t i m u l i a n d s h o u l d be e x a m i n e d a s s e p a r a t e e n t i t i e s . The f o c u s o f t h i s s t u d y i s on t h e m u l t i f a m i l y h o u s i n g s u b m a r k e t . W i t h i n t h e m u l t i f a m i l y m a r k e t , v a c a n c y r a t e s a r e c i t e d a s a key i n d i c a t o r o f demand. A s s u m i n g t h a t t h e m a r k e t i s e f f i c i e n t a n d h a s some l o n g r u n e q u i l i b r i u m p o i n t , an i n c r e a s e i n demand s h o u l d r e s u l t i n a d e c l i n e i n v a c a n c i e s , an i n c r e a s e i n r e n t s a n d s u b s e q u e n t i n c r e a s e i n new s t o c k . H owever, t h r o u g h o u t t h e 1970's t h e r e have been c o n s i s t e n t l y l o w v a c a n c y r a t e s i n a l l m a j o r c e n t r e s i n Canada and s i m u l t a n e o u s d e c l i n e s i n t h e l e v e l o f m u l t i f a m i l y u n i t s t a r t s . I n V a n c o u v e r v a c a n c y r a t e s were b e l o w one p e r c e n t f o r much o f t h e p e r i o d f r o m 1974 t o 1981, b u t s t a r t s d e c l i n e d f r o m 2,962 i n t h e f o u r t h q u a r t e r o f 1973 t o a l o w o f 213 u n i t s i n t h e f o u r t h q u a r t e r o f 1982. I t may be a r g u e d t h a t t h i s a p p a r e n t d i s e q u i l i b r i u m i s t h e r e s u l t o f r e n t c o n t r o l s ; p r i c e s were n o t p e r m i t t e d t o f i n d t h e i r m a r k e t l e v e l s a n d c o n s e q u e n t l y s u p p l y f a i l e d t o r e s p o n d t o t h e i n c r e a s e d demand. C o u n t e r t o t h i s , e v i d e n c e i n d i c a t e s t h a t s i m i l a r d e c l i n e s i n c o n s t r u c t i o n were n o t e d i n c i t i e s w i t h o u t c o n t r o l s ( s e e J o n e s , 1 9 8 3 , p 6 ) . R e c e n t comments f r o m m a r k e t 3 p a r t i c i p a n t s i n d i c a t e t h a t t h e u n c e r t a i n t y and l o w i n v e s t m e n t r e t u r n s i n t h e . r e n t a l m a r k e t have d i s c o u r a g e d i n v e s t m e n t . T h e r e f o r e , t h e m a r k e t d y n a m i c s r e q u i r e s i n v e s t i g a t i o n b e y o n d t h e s i m p l i s t i c a s s u m p t i o n t h a t v a c a n c y r a t e s r e f l e c t demand c o n d i t i o n s a n d b u i l d e r s w i l l r e s p o n d t o t h e s e c h a n g e s i n t h e l o n g t e r m . The d y n a m i c s o f t h e m u l t i f a m i l y h o u s i n g m a r k e t h a v e been f u r t h e r c l o u d e d by g o v e r n m e n t i n t e r v e n t i o n i n t h e m a r k e t and p o l i c y i m p l e m e n t a t i o n . T h e s e have been i n t e n s i f i e d d u r i n g t h e 1970's w i t h d i r e c t s u b s i d y p r o g r a m s , s u b s i d i z e d r e n t a l p r o g r a m s a n d c h a n g e s i n t h e t a x l e g i s l a t i o n . The b a s i c r a t i o n a l e h a s been t h a t w i t h o u t s u c h p o l i c y , t h e m a r k e t w o u l d be u n w i l l i n g t o s u p p l y " a d e q u a t e and a f f o r d a b l e " r e n t a l u n i t s ( W e i c h e r , 1 9 7 6 ) . Low l e v e l s o f m u l t i f a m i l y s t a r t s , c o n s i s t e n t l y l o w v a c a n c y r a t e s and t h e p e r c e i v e d n e e d f o r g o v e r n m e n t i n t e r v e n t i o n h a v e l e n t s u p p o r t t o t h e b e l i e f t h a t t h e r e i s a r e n t a l h o u s i n g c r i s i s i n most C a n a d i a n u r b a n c e n t r e s . B u t i t i s a l s o p o s s i b l e t h a t t h e s t r u c t u r e o f t h e h o u s i n g m a r k e t i s c h a n g i n g a n d t h i s a l a r m may be p r e m a t u r e . D e c l i n i n g h o u s e h o l d s i z e , l o w e r b i r t h r a t e s , a g r e a t e r demand f o r i n n e r c i t y l o c a t i o n s a n d t h e u s e o f h o u s i n g a s an i n v e s t m e n t s u g g e s t t h a t t h e m a r k e t i s u n d e r g o i n g a d j u s t m e n t , r a t h e r t h a n a c r i s i s . The r e s p o n s e o f m a r k e t p a r t i c i p a n t s t o t h e s e c h a n g e s i s s l o w a n d w i l l t h e r e f o r e be n o t e d i n t h e l o n g t e r m c y c l e b u t may n o t be r e f l e c t e d i n t h e o v e r l a p p i n g s h o r t c y c l e o f t h e m a r k e t . G i v e n t h e i n a b i l i t y o f v a c a n c y r a t e s t o e x p l a i n t h e c y c l e i n h o u s i n g c o n s t r u c t i o n a n d t h e p o s s i b i l i t y o f t h e m a r k e t 4 undergoing a process of adjustments, t h i s paper proposes the use of i n v e n t o r i e s as a l i n k between the demand f o r and supply of mu l t i f a m i l y u n i t s . The m u l t i f a m i l y c o n s t r u c t i o n c y c l e c o n s i s t s of two components; the long c y c l e which i s responding to changing demographics and market s t r u c t u r e ; and the short c y c l e which r e f l e c t s the more immediate economic c o n d i t i o n s . The a b i l i t y of b u i l d e r s or i n v e s t o r s to maintain i n v e n t o r i e s of completed and unoccupied u n i t s p r o v i d e s a b u f f e r to absorb any u n a n t i c i p a t e d changes i n demand. The s p e c i f i c l e v e l of inventory h e l d , at any time, w i l l r e f l e c t expected demand and cu r r e n t economic c o n d i t i o n s . T h i s i s s i m i l a r to manufacturing invento r y c y c l e s and p r i c i n g mechanisms, but the immobility and d u r a b i l i t y of housing make i t a unique commodity, r e s t r i c t i n g the a p p l i c a t i o n of in v e n t o r y adjustment theory. Rather than e s t i m a t i n g the l e v e l of s t a r t s with only economic v a r i a b l e s , the suggested approach i s to i n c o r p o r a t e demographic change and i n v e n t o r i e s i n t o the model. Assuming b u i l d e r s or i n v e s t o r s have some d e s i r e d l e v e l of i n v e n t o r i e s based on economic c o n d i t i o n s and expected demand from demographic change, the l e v e l of s t a r t s w i l l be set to maintain i n v e n t o r i e s at t h i s l e v e l and to s a t i s f y expected demand. C l e a r l y f l u c t u a t i o n s between the a c t u a l and d e s i r e d l e v e l of i n v e n t o r i e s w i l l e x i s t from u n a n t i c i p a t e d changes i n demand and the i n a b i l i t y to a d j u s t i n v e n t o r i e s immediately. Gradual adjustments f o r u n a n t i c i p a t e d demand changes and f l u c t u a t i o n s i n the d e s i r e d i n v e n t o r y l e v e l w i l l generate the noted c y c l e i n s t a r t s . T h i s paper w i l l develop the t h e o r e t i c a l s t r u c t u r e of t h i s 5 t e c h n i q u e a n d r e p o r t t h e e m p i r i c a l a n a l y s i s u s i n g V a n c o u v e r C e n s u s M e t r o p o l i t a n A r e a d a t a f r o m 1963 t o 1 9 8 2 . I n t h i s d e v e l o p m e n t o f a r e g i o n a l i n v e n t o r y a d j u s t m e n t m o d e l f o r t h e m u l t i f a m i l y h o u s i n g m a r k e t , t w o m a i n q u e s t i o n s w i l l b e a d d r e s s e d : 1. A r e t h e r e i d e n t i f i a b l e c a u s e s f o r t h e d e c l i n e i n r e n t a l a p a r t m e n t d e v e l o p m e n t a n d o f t h e a t t e n d a n t d e c l i n e i n v a c a n c y r a t e s i n U r b a n C a n a d a d u r i n g t h e 1 9 7 0 ' s ? 2. A r e d e v e l o p e r s / b u i l d e r s r e s p o n d i n g t o a n i n v e n t o r y c y c l e w i t h i n t h e h o u s i n g m a r k e t ? Do s t a r t s t h e r e f o r e r e f l e c t t h e d e s i r e d l e v e l o f i n v e n t o r i e s i n e a c h p e r i o d b a s e d o n o t h e r e c o n o m i c c o n d i t i o n s ? T h e n e x t c h a p t e r w i l l b r i e f l y o u t l i n e t h e c u r r e n t s t a t e o f t h e a r t i n h o u s i n g s t a r t s m o d e l s . I n r e c o g n i t i o n o f t h e i m p a c t g o v e r n m e n t p o l i c y h a s h a d o n t h e h o u s i n g m a r k e t , C h a p t e r 3 w i l l p r e s e n t a summary o f t h o s e p o l i c i e s m o s t d i r e c t l y i n f l u e n c i n g t h e m u l t i f a m i l y h o u s i n g m a r k e t i n V a n c o u v e r . C h a p t e r 4 w i l l d i s c u s s t h e i n v e n t o r y a d j u s t m e n t c o n c e p t a n d t h e t h e o r e t i c a l m o d e l d e v e l o p e d i n t h i s p a p e r . C h a p t e r 5 w i l l d i s c u s s t h e d a t a s e r i e s a n d t h e i n h e r e n t d i f f i c u l t i e s w i t h t h e s e d a t a . C h a p t e r 6 w i l l p r e s e n t t h e e m p i r i c a l r e s u l t s o f t h e m o d e l , a t i m e s e r i e s m o d e l b a s e d o n t h e d a t a a n d t h e t e s t i n g o f t h e m o d e l ' s r e l i a b i l i t y a n d f o r e c a s t i n g a b i l i t y . A summary o f t h e f i n d i n g s a n d t h e i m p l i c a t i o n s - f o r f u r t h e r r e s e a r c h a r e o u t l i n e d i n C h a p t e r 7. 6 2. LITERATURE REVIEW The e x i s t i n g l i t e r a t u r e on h o u s i n g s t a r t s a n d t h e s t r u c t u r e o f h o u s i n g m a r k e t s may be d i v i d e d i n t o f o u r b r o a d c a t e g o r i e s . E s s e n t i a l l y , t h e s e encompass d i s c u s s i o n s o f (1) c y c l e s i n r e s i d e n t i a l c o n s t r u c t i o n , (2) t h e p r i c e a n d income e l a s i t i c i t i e s o f h o u s i n g demand a n d s u p p l y , ( 3 ) t h e r a t i o n a l e a n d i m p l i c a t i o n s o f g o v e r n m e n t p o l i c y and i n t e r v e n t i o n i n t h e h o u s i n g . m a r k e t , (4) e c o n o m e t r i c m o d e l s o f t h e m a r k e t and e s t i m a t i o n s o f h o u s i n g s t a r t s a n d demand. .-> The l i t e r a t u r e on h o u s i n g c y c l e s t e n d s t o be v e r y g e n e r a l and d e s c r i p t i v e , w i t h l a t e r s t u d i e s e x a m i n i n g t h e s p e c i f i c f o r c e s o f t h e s e c y c l e s a n d t h e d e v e l o p m e n t o f e c o n o m e t r i c m o d e l s . S i n c e t h e s e p r o v i d e b a c k g r o u n d f o r t h e e c o n o m e t r i c a n a l y s i s r e v i e w e d , t h e g e n e r a l c o n c e p t s a n d t h e o r i e s o f h o u s i n g c y c l e s w i l l be p r e s e n t e d . T h e r e i s no c o n c e n s u s i n t h e l i t e r a t u r e on t h e p r i c e o r income e l a s t i c i t i e s o f demand o r s u p p l y ; e s t i m a t e s r a n g e f r o m n e a r z e r o t o i n f i n i t y ( s e e R y d e l l , 1 9 8 1 , p 3 ) . A t t e m p t i n g t o r e c o n c i l e t h e s e d i f f e r e n c e s , s t u d i e s have d i s t i n g u i s h e d b e t ween r e n t e r s a n d o w n e r s , low a n d h i g h income g r o u p s , on t h e p r e m i s e t h a t an u n d e r s t a n d i n g of t h e s e e l a s t i c i t i e s a n d t h e d i f f i c u l t i e s i n t h e i r e s t i m a t i o n s w i l l p r o v i d e a b e t t e r u n d e r s t a n d i n g o f t h e m a r k e t a n d i t s p a r t i c i p a n t s . The r e s u l t s o f t h i s l i t e r a t u r e w i l l be r e v i e w e d b r i e f l y . G o v e r n m e n t p o l i c y a n d i n t e r v e n t i o n w i l l u n d o u b t e d l y a f f e c t t h e r e s u l t s o f any e m p i r i c a l a n a l y s i s . However, t h i s l i t e r a t u r e 7 d o e s n o t p r o v i d e any b a c k g r o u n d f o r t h e t h e o r e t i c a l m o d e l . A s e p a r a t e c h a p t e r i s d e v o t e d t o d i s c u s s i o n o f C a n a d i a n Government h o u s i n g p o l i c y a n d i t s i m p a c t on t h e m u l t i f a m i l y h o u s i n g m a r k e t . F i n a l l y , an i n c r e a s i n g e m p h a s i s h a s been p l a c e d on t h e d e v e l o p m e n t o f e c o n o m e t r i c m o d e l s t o e x p l a i n a n d / o r p r e d i c t h o u s i n g s t a r t s . The s p e c i f i c n a t u r e o f p r e v i o u s e c o n o m e t r i c m o d e l s a nd t h e e s t i m a t i o n t e c h n i q u e s a r e o f g r e a t s i g n i f i c a n c e t o t h e a l t e r n a t e a p p r o a c h p r o p o s e d i n t h i s p a p e r . The e m p h a s i s of t h i s c h a p t e r w i l l be on t h e d e v e l o p m e n t a n d s u c c e s s o f e x i s t i n g h o u s i n g s t a r t s m o d e l s , w i t h f o u r s p e c i f i c m o d e l s d i s c u s s e d a s b a c k g r o u n d t o t h e t h e o r e t i c a l m o d e l p r e s e n t e d i n C h a p t e r 4. 2.1 HOUSING CYCLES Some a r g u e t h a t t h e h o u s i n g c y c l e i s a n t i c y c l i c a l t o t h e g e n e r a l b u s i n e s s c y c l e ( G u t t e n t a g , 1 9 6 1 ; A l b e r t s , 1 9 6 2 ) . O t h e r s m a i n t a i n t h a t a l t h o u g h t h e h o u s i n g c y c l e d o e s n o t m a t c h t h e g e n e r a l c y c l e , i t i s n o t a n t i c y c l i c a l , r a t h e r , i t has a d i f f e r e n t t i m e h o r i z o n ( C h u n g , 1 9 7 6 ; S t e v e n s , 1 9 7 6 ) . The d u r a t i o n and a m p l i t u d e o f t h e c y c l e s a r e u s u a l l y m e a s u r e d by t h e p e a k s a n d t r o u g h s , a l t h o u g h i t i s a l s o p o s s i b l e t o u s e d e v i a t i o n s f r o m t h e e x p e c t e d t r e n d a s a m e a s u r e o f v o l a t i l i t y . The f o r m e r m e a s u r e i s g e n e r a l l y u s e d i n t h e l i t e r a t u r e on h o u s i n g c y c l e s a nd i s t h e r e l e v a n t m e asure i n t h e f o l l o w i n g d i s c u s s i o n . S u p p o r t f o r t h e h o u s i n g c y c l e b e i n g a n t i c y c l i c a l i s o f f e r e d by e v i d e n c e i n t h e U n i t e d S t a t e s d u r i n g t h e p o s t w a r p e r i o d . 8 Housing c o n s t r u c t i o n d e c l i n e d d u r i n g the p e r i o d s of business expansion from 1945 to 1948, again u n t i l mid-1953, and from l a t e 1954 to l a t e 1957. S i m i l a r l y , during the r e c e s s i o n s of 1948 to 1949 and 1953 to 1954, the housing c y c l e was on an upswing. More recent Canadian trends have not supported the a n t i c y c l i c a l theory as s t r o n g l y ; the business c y c l e peaked i n 1965 and 1968, but r e s i d e n t i a l c o n s t r u c t i o n was at a low i n 1965 and c l o s e to a peak i n 1968 (Chung, 1976,p34). I t i s g e n e r a l l y accepted that r e s i d e n t i a l c o n s t r u c t i o n i s c y c l i c a l and that t h i s c y c l e does not correspond to the business c y c l e , nor does i t f o l l o w the n o n - r e s i d e n t i a l c o n s t r u c t i o n c y c l e (see Chung,1976,pp35-6). S e v e r a l t h e o r i e s have been proposed to e x p l a i n these c y c l e s , f o c u s i n g on c r e d i t c o n d i t i o n s and the demographic s t r u c t u r e of the p o p u l a t i o n . The cost and a v a i l a b i l i t y of c r e d i t c l e a r l y i n f l u e n c e r e s i d e n t i a l c o n s t r u c t i o n . I n t e r e s t r a t e s represent the cost of c r e d i t and the p o t e n t i a l y i e l d i n both the bond and mortgage markets, thereby i n f l u e n c i n g the flow of funds between the two markets. S u c c i n c t l y , as the y i e l d on bonds i n c r e a s e s , funds w i l l move i n t o t h i s market at the expense of the mortgage market. 1 Since the flow of funds w i l l r e s t r i c t a c t i v i t y i n each market, the l o g i c a l c o n c l u s i o n i s that housing and the general b usiness investment c y c l e s w i l l be a n t i c y c l i c a l . But t h i s ignores the g r e a t e r complexity of the mortgage market. I n t e r e s t r a t e s do not f u l l y r e f l e c t o r i g i n a t i o n or other fees r e q u i r e d by the l e n d e r . Mortgages f o r l a r g e r p r o j e c t s have t h e i r own i n d i v i d u a l c h a r a c t e r i s t i c s and t h e r e f o r e they are not comparable 9 simply on the b a s i s of i n t e r e s t r a t e s . F u r t h e r , the flow of funds from the mortgage market w i l l be c o n s t r a i n e d by p r i o r loan commitments by l e n d e r s . 2 I t i s a l s o p o s s i b l e f o r le n d e r s i n the mortgage market to i n f l u e n c e borrowing, and subsequently c o n s t r u c t i o n a c t i v i t y , through the a v a i l a b i l i t y of c r e d i t by adjustments i n l o a n - t o - v a l u e r a t i o s , the a m o r t i z a t i o n p e r i o d or the term. Each w i l l a f f e c t the r e q u i r e d mortgage payment, the r e s u l t a n t p r o f i t a b i l i t y of the p r o j e c t and consequently, c o n s t r u c t i o n a c t i v i t y . O bviously, the expected y i e l d s i n the bond and mortgage markets w i l l i n f l u e n c e the q u a n t i t y of funds a v a i l a b l e f o r investment in each market, but i n t e r e s t r a t e s alone are i n s u f f i c i e n t to e x p l a i n the noted c y c l e s . A l t e r n a t i v e l y , the l e v e l of c o n s t r u c t i o n a c t i v i t y w i l l be i n f l u e n c e d by the demographic s t r u c t u r e , r i s i n g incomes, changing s o c i a l values and r e l a t i v e p r i c e s f o r s i n g l e and multi f a m i l y housing u n i t s . 3 From 1953 to 1973, the r a t i o of mul t i f a m i l y to s i n g l e f a m i l y s t a r t s i n the United S t a t e s trended upward to a peak of 83 percent i n the t h i r d q u a r t e r of 1973. T h i s f e l l to 32 percent by the f i r s t q u a r t e r of 1975. Although new housing c o n s t r u c t i o n was i n c r e a s i n g from e a r l y 1975, apartment c o n s t r u c t i o n d i d not recover to the same extent, and has remained at about 30 percent of t o t a l s t a r t s . The increase in m u l t i f a m i l y c o n s t r u c t i o n from 1959 to 1973 has been a t t r i b u t e d to the movement of the "baby boom" p o p u l a t i o n i n t o the 15 to 29 age coho r t . The i n d u s t r y responded to the expected i n c r e a s e i n demand f o r r e n t a l u n i t s by i n c r e a s i n g m u l t i f a m i l y c o n s t r u c t i o n . As t h i s , "bubble" i n the p o p u l a t i o n ages, the 10 demand f o r s i n g l e f a m i l y u n i t s i s e x p e c t e d t o i n c r e a s e , b u t t h e m u l t i f a m i l y r e n t a l m a r k e t i s l e s s l i k e l y t o r e b o u n d . S t e v e n s s u g g e s t s t h a t t h e c o n s i s t e n t d e c l i n e i n s t a r t s s i n c e 1975 may be t h e r e s u l t o f " o v e r b u i l d i n g " a p a r t m e n t u n i t s i n t h e boom p e r i o d o f 1971 t o 1972 ( 1 9 7 6 , p . 1 8 ) . The e v i d e n c e i n d i c a t e s t h a t t h e r e l a t i o n s h i p may be more c o m p l e x t h a n two i n t e r a c t i v e c y c l e s a n d t h e r e f o r e , i n v e s t i g a t i o n must e x t e n d b e y o n d e x p l a i n i n g t h e l i n k b e t w e e n t h e s e c y c l e s . S t u d i e s s u g g e s t t h a t c o n s t r u c t i o n c y c l e s r a n g e f r o m 16 t o 20 y e a r s , w h i l e b u s i n e s s c y c l e s r a n g e f r o m 8 t o 12 y e a r s ( C h u n g , 1 9 7 6 , p 3 5 ) . F u r t h e r , t h e r e may be l o n g a n d s h o r t c y c l e s w i t h i n t h e h o u s i n g m a r k e t . G u t t e n t a g ( 1 9 61) s u g g e s t s t h a t t h e l o n g c y c l e s a r e t h e r e s u l t o f f l u c t u a t i o n s i n t h e demand f o r h o u s i n g a n d t h e s h o r t c y c l e s a r e more c l o s e l y l i n k e d t o t h e m o r t g a g e m a r k e t . C o n s e q u e n t l y , i f demand i s i n f l u e n c i n g c h a n g e s i n t h e l e v e l o f c o n s t r u c t i o n , m o r t g a g e y i e l d s a n d c o n s t r u c t i o n s h o u l d move i n t h e same d i r e c t i o n . A l t e r n a t i v e l y , m o r t g a g e y i e l d s and c o n s t r u c t i o n l e v e l s w o u l d be e x p e c t e d t o move i n o p p o s i t e d i r e c t i o n s when t h e s u p p l y o f c r e d i t i s i n f l u e n c i n g t h e m a r k e t . U n d o u b t e d l y , t h e d e m o g r a p h i c s t r u c t u r e a n d e c o n o m i c c o n d i t i o n s w i l l i n f l u e n c e t h e demand f o r s p e c i f i c t y p e s o f u n i t s a n d t h e r e s p o n s i v e n e s s o f b u i l d e r s , h o w e v e r , t h e m a g n i t u d e o f t h e i m p a c t s a t t r i b u t a b l e t o d i f f e r e n t f o r c e s a n d s t i m u l i r e q u i r e s f u r t h e r i n v e s t i g a t i o n . 2.2 SUPPLY OF HOUSING - E L A S T I C I T I E S The s u p p l y o f h o u s i n g o b v i o u s l y r e f e r s t o t h e q u a n t i t y o f 11 h o u s i n g s e r v i c e s a v a i l a b l e i n t h e m a r k e t . S i m i l a r l y , t h e demand i s t h e q u a n t i t y o f s e r v i c e s t h a t t h e p o p u l a t i o n r e q u i r e s a t any g i v e n p o i n t i n ' t i m e . The p r i c e e l a s t i c i t y o f t h e h o u s i n g s u p p l y i s t h e n t h e p e r c e n t a g e c h a n g e i n t h e q u a n t i t y o f h o u s i n g s e r v i c e s p r o v i d e d , a s s o c i a t e d w i t h a one p e r c e n t i n c r e a s e i n t h e p r i c e o f t h o s e s e r v i c e s . S i m i l a r d e f i n i t i o n s c a n be d e r i v e d f o r t h e i n c o m e e l a s t i c i t y o f s u p p l y , a n d t h e p r i c e a n d income e l a s t i c i t i e s o f demand. B u t , w i t h i n a l l o f t h e s e , t h e r e i s no c l e a r d e f i n i t i o n o f ' h o u s i n g s e r v i c e s ' . S t a n d a r d i z a t i o n o f t h e q u a n t i t y o f h o u s i n g s e r v i c e s h a s been a c h i e v e d by u s i n g some r e n t a l i n d e x , c o s t s o f i n p u t s , o r s t a n d a r d h o u s e p r i c e i n r e c o g n i t i o n o f t h e v a r y i n g q u a l i t i e s o f h o u s i n g a v a i l a b l e i n t h e m a r k e t . T h e r e i s g e n e r a l a g r e e m e n t i n t h e l i t e r a t u r e t h a t t h e p r i c e e l a s t i c i t y o f demand f o r h o u s i n g i s b e t w e e n 0.17 and 1.28 ( R y d e l l , 1 9 8 1 , p 2 1 ) . F o l l a i n ( 1 9 7 9 ) s u g g e s t s t h a t t h i s may r e f l e c t t h e p r i c e e l a s t i c i t y o f demand f o r t h e o v e r a l l p o p u l a t i o n , b u t l o w - i n c o m e , r e n t a l h o u s e h o l d s a r e much l e s s r e s p o n s i v e t o c h a n g e s i n p r i c e o r i n c o m e . T h i s r a i s e s t h e q u e s t i o n o f w h e t h e r t h e e l a s t i c i t i e s s h o u l d be m e a s u r e d f o r t h e t o t a l p o p u l a t i o n , o r w h e t h e r i t more a p p r o p r i a t e t o d i s a g g r e g a t e t h e p o p u l a t i o n by income and t e n u r e . The l i t e r a t u r e o f f e r s l e s s a g r e e m e n t a b o u t t h e p r i c e e l a s t i c i t y o f s u p p l y . R y d e l l ( l 9 8 1 ) a t t e m p t s t o r e c o n c i l e some o f t h e d i f f e r e n c e s by e x a m i n i n g t h e d a t a u s e d , o r d e f i n i t i o n s o f t h e h o u s i n g s t o c k , w h i c h may a f f e c t t h e r e s u l t s s i g n i f i c a n t l y . T h i s p r o v i d e s an e x p l a n a t i o n o f t h e d i v e r g e n t e s t i m a t e s , b u t 12 s t i l l l e a v e s no c o n c e n s u s o f t h e " c o r r e c t " m e a sure o f e l a s t i c i t y o f s u p p l y . B a s e d on a s a m p l e o f 59 m e t r o p o l i t a n c e n t r e s i n t h e U n i t e d S t a t e s , R y d e l l s u g g e s t s t h a t t h e l o n g r u n p r i c e e l a s t i c i t y i s 11.3, and t h e s h o r t r u n o r o c c u p a n c y r a t e p r i c e e l a s t i c i t y i s 0.2 where t h e v a c a n c y r a t e i s 3 p e r c e n t , a n d 2.0 where t h e v a c a n c y r a t e i s 15 p e r c e n t ( I 9 8 l , p 2 ) . The d i s t i n c t i o n i s t h a t i n t h e l o n g r u n , s u p p l y i s f l e x i b l e a nd c a n a d j u s t t o demand c h a n g e s ; i n t h e s h o r t r u n t h e o n l y a d j u s t m e n t i s i n t h e number o f u n i t s o c c u p i e d a n d t h e t o t a l s u p p l y d o e s n o t a d j u s t . T h i s d o e s n o t a d d r e s s t h e q u e s t i o n o f s e p a r a t e e l a s t i c i t i e s f o r r e n t a l o r o w n e r - o c c u p i e d u n i t s . Do b u i l d e r s r e s p o n d d i f f e r e n t l y t o p r i c e s a n d o t h e r s t i m u l i i n e a c h o f t h e s e m a r k e t s ? E v i d e n c e p r e s e n t e d i n t h e d e v e l o p m e n t o f e c o n o m e t r i c m o d e l s s u g g e s t s t h a t i n f a c t t h e two m a r k e t s a r e v e r y d i s t i n c t . 2.3 HOUSING STARTS MODELS The c y c l i c a l n a t u r e o f t h e r e s i d e n t i a l c o n s t r u c t i o n i n d u s t r y and t h e m a r k e t a d j u s t m e n t m e chanisms have been d i s c u s s e d e x t e n s i v e l y i n s e v e r a l t h e o r e t i c a l a n d e m p i r i c a l a n a l y s e s . The f o c u s o f t h e s e h a s r a n g e d f r o m n a t i o n a l e c o n o m i c m o d e l s where h o u s i n g i s an i n t e g r a l p a r t ( S m i t h , 1 9 6 9 ; W a s l a n d e r , 1 9 7 3 ) t o r e g i o n a l m o d e l s ( R o s e n , 1 9 7 9 ) , and f r o m v i e w i n g t h e h o u s i n g m a r k e t a s a w h o l e ( M a i s e l , 1 9 6 3 ; J a f f e e & R o s e n , 1979; F a i r , 197.2) t o d i s a g g r e g a t i n g t h e m u l t i and s i n g l e f a m i l y m a r k e t s ( S m i t h , 1 9 6 9 ) . D e s p i t e t h e s e d i f f e r e n c e s , c r e d i t a n d f i n a n c i a l v a r i a b l e s a r e c o n s i s t e n t l y s i n g l e d o u t t o be t h e key i n e x p l a i n i n g m a r k e t f l u c t u a t i o n s . Some o t h e r d e t e r m i n a n t s 1 3 w h i c h h a v e been i n c o r p o r a t e d i n t o m o d e l s i n c l u d e c h a n g e i n p o p u l a t i o n ( i n c r e a s e o r d e c r e a s e ; a g e - s e x b r e a k d o w n ; h o u s e h o l d f o r m a t i o n , m i g r a t i o n ) , i ncome a n d e m p l o y m e n t , c o n s u m e r a s s e t h o l d i n g s , t h e p r i c e o f h o u s i n g , o c c u p a n c y c o s t s , c o n s u m e r t a s t e s and p r e f e r e n c e s , t h e c o n d i t i o n o f e x i s t i n g s t o c k a n d t h e r e s p o n s i v e n e s s o f b u i l d e r s a n d i n v e s t o r s t o c h a n g e s i n demand ( G r e b l e r & M a i s e l , 1 9 6 3 , p p 7 6 - 7 ) . The a s s u m p t i o n s o f t h e u n d e r l y i n g m a r k e t s t r u c t u r e f o l l o w two m a j o r a p p r o a c h e s . The f i r s t a s s u mes t h a t t h e r e i s some l o n g r u n e q u i l i b r i u m i n t h e h o u s i n g m a r k e t . P r i c e a n d s u p p l y t h e n r e s p o n d t o c h a n g e s i n t h e m a r k e t i n a c c o r d a n c e t o c l a s s i c a l e c o n o m i c t h e o r y , a t t e m p t i n g t o a c h e i v e t h i s e q u i l i b r i u m p o i n t . The f l u c t u a t i o n s i n t h e s u p p l y r e s u l t i n t h e n o t e d c y c l e s i n c o n s t r u c t i o n ( Q u i g l e y , 1 9 7 8 ) . The s e c o n d a p p r o a c h assumes d i s e q u i l i b r i u m i n t h e h o u s i n g m a r k e t . To a n a l y s e t h e m a r k e t f o r c e s i t i s n e c e s s a r y t o f i r s t d e t e r m i n e w h e t h e r s u p p l y o r demand i s c o n s t r a i n i n g t h e m a r k e t a d j u s t m e n t p r o c e s s a t any g i v e n t i m e ( s e e F a i r , 1 9 7 2 ; F a i r & J a f f e e , 1 9 7 2 ) . I n r e s p o n s e t o t h e s e d i v e r s e a p p r o a c h e s , S m i t h s u g g e s t s t h a t t h e a s s u m p t i o n o f l o n g r u n e q u i l i b r i u m may be c o r r e c t , b u t s t u d i e s s h o u l d c o n c e n t r a t e on t h e p r o c e s s o f a d j u s t m e n t s i n t h e m a r k e t a s i t a p p r o a c h e s e q u i l i b r i u m , n o t t h e f i n a l e q u i l i b r i u m r e s u l t . " The f o u r m o d e l s d i s c u s s e d h e r e p r o v i d e an o v e r v i e w o f t h e ' s t a t e o f t h e a r t ' i n e s t i m a t i n g h o u s i n g s t a r t s . E a c h o f t h e s e m o d e l s assumes some l o n g r u n e q u i l i b r i u m i n t h e h o u s i n g m a r k e t an d t h a t t h e m a r k e t i s e f f i c i e n t . They by no means e x h a u s t t h e e x i s t i n g w o r k , b u t do i n d i c a t e t h e g e n e r a l t r e n d s i n h o u s i n g 14 s t a r t s m o d e l s . 2.3.1 M a i s e l - I n v e n t o r y A d j u s t m e n t M o d e l M a i s e l ' s model i s b a s e d on t h e s u p p o s i t i o n t h a t i n v e n t o r y c y c l e s i n t h e h o u s i n g m a r k e t a r e s i m i l a r t o t h e c y c l e s n o t e d i n m a n u f a c t u r i n g . V o l a t i l i t y i n t h e l e v e l o f s t a r t s i s n o t a t t r i b u t e d t o c r e d i t c o n d i t i o n s a n d c o s t s , b u t i n v e n t o r i e s and r e s p o n s e s o f m a r k e t p a r t i c i p a n t s . The a d j u s t m e n t p r o c e s s f o r u n i t s t a r t s a n d i n v e n t o r y l e v e l s i n v o l v e s a s e r i e s o f l a g s and p a r t i a l a d j u s t m e n t s w h i c h f o s t e r i n s t a b i l i t y i n t h e s y s t e m . The b a s i c a r g u m e n t o f M a i s e l ' s m o d e l s t a t e s t h a t , a s s u m i n g t h e h o u s i n g m a r k e t i s i n e q u i l i b r i u m , b u i l d e r s w o u l d i n i t i a t e h o u s i n g s t a r t s s u f f i c i e n t t o m a i n t a i n a c o n s t a n t l e v e l o f i n v e n t o r y . T h e r e f o r e , t h e c o m p l e t i o n o f u n i t s w o u l d e x a c t l y e q u a l demand; s t o c k w o u l d i n c r e a s e by t h e number o f c o m p l e t i o n s , l e s s a n y r e m o v a l s o r d e m o l i t i o n s . I t i s t h e n p o s s i b l e f o r some e x o g e n e o u s f o r c e t o i n i t i a t e c h a n g e i n t h e r a t e o f h o u s e h o l d f o r m a t i o n , an i n c r e a s e o r d e c r e a s e i n t h e number o f d e m o l i t i o n s , o r c h a n g e b u i l d e r e x p e c t a t i o n s o f f u t u r e demand a n d / o r p r o f i t . The r e s u l t a n t d i s e q u i l i b r i u m i n t h e s y s t e m w i l l be n o t e d i n t e r n a l l y t h r o u g h v a c a n c y r a t e s a n d t h e r e l a t i v e p r i c e s f o r r e n t a l a n d o w n e r s h i p u n i t s . S u b s e q u e n t l y , - b u i l d e r s ' p r o f i t s w i l l be a f f e c t e d d i r e c t l y by p r i c e f l u c t u a t i o n s , o r i n d i r e c t l y t h r o u g h t h e h o l d i n g c o s t s o f v a c a n t u n i t s , u n e x p e c t e d c h a n g e s i n demand (by i n c r e a s e d o r r e d u c e d r a t e s o f h o u s e h o l d f o r m a t i o n ) . I f c o n d i t i o n s a r e f a v o u r a b l e , s t a r t s s h o u l d i n c r e a s e u n t i l v a c a n c i e s b e g i n t o i n c r e a s e . T h i s r i s e i n v a c a n c y r a t e s and 15 i n v e n t o r y l e v e l s w i l l f e e d b a c k t h r o u g h t h e s y s t e m u n t i l t h e l e v e l o f s t a r t s d e c r e a s e s . T h i s o n g o i n g f e e d b a c k m e c h a n i s m w i l l g e n e r a t e t h e i n v e n t o r y c y c l e a n d c a u s e t h e n o t e d v o l a t i l i t y i n s t a r t s . G i v e n t h e b a s i c f r a m e w o r k f o r t h e h o u s i n g m a r k e t , M a i s e l s u g g e s t s a m o d e l b a s e d on f o u r f u n c t i o n a l e q u a t i o n s a n d a f i n a l i d e n t i t y f o r s t a r t s . T h e l e v e l o f s t a r t s i n a n y p e r i o d w i l l e q u a l t h e sum o f n e t h o u s e h o l d f o r m a t i o n , n e t r e m o v a l s , c h a n g e s i n i n v e n t o r i e s a n d d e v i a t i o n s i n v a c a n c i e s f rom t h e e x p e c t e d t r e n d . Ne t h o u s e h o l d f o r m a t i o n f o r m s t h e d e m o g r a p h i c c o m p o n e n t o f t h e m o d e l . C h a n g e s i n t h e number o f h o u s e h o l d s w i l l d e p e n d upon t h e p o p u l a t i o n s t r u c t u r e , i n c o m e s , u n e m p l o y m e n t , c r e d i t a n d p r i c e s . T h i s i s c o n s i s t e n t w i t h o t h e r m o d e l s t h a t e x a m i n e c h a n g e s i n h o u s e h o l d f o r m a t i o n . T i m e a n d d i s t u r b a n c e t e r m s a r e a d d e d t o a c c o u n t f o r any v a r i a t i o n n o t e x p l a i n e d by t h e o t h e r v a r i a b l e s . N e t r e m o v a l s a r e g i v e n a s f l u c t u a t i n g i n a c c o r d a n c e w i t h g o v e r n m e n t p o l i c y a n d p r o g r a m s w h i c h may e n c o u r a g e o r d i s c o u r a g e new c o n s t r u c t i o n , i n c o m e l e v e l s , e x i s t i n g v a c a n c i e s a n d t h e s t o c k o f h o u s i n g . T h e d i f f i c u l t y i n m e a s u r i n g t h e s e i m p a c t s and t h e l e v e l o f r e m o v a l s i n a n y t i m e p e r i o d p r e v e n t e d t h e s e f r o m b e i n g i n c l u d e d i n M a i s e l ' s e m p i r i c a l a n a l y s i s . V a c a n c i e s a r e t h o u g h t t o f l u c t u a t e a b o u t a t r e n d . M a i s e l m e a s u r e d t h e d e v i a t i o n o f v a c a n c y r a t e s f r o m t h i s t r e n d , a n d c o n c l u d e d t h e s e were a f u n c t i o n o f c o s t s , h o u s e h o l d a n d b u i l d e r m a r k e t e x p e c t a t i o n s , c r e d i t a v a i l a b i l i t y a n d p r i c e s , r e n t s a n d t h e e x i s t i n g d i s e q u i l i b r i u m i n v a c a n c i e s . I n v e n t o r i e s a r e i n c l u d e d t o i n c o r p o r a t e t h e t i m e l a g b e t w e e n s t a r t s and 16 c o m p l e t i o n s . The c h a n g e i n i n v e n t o r i e s w i l l be a f u n c t i o n o f s t a r t s and c o m p l e t i o n s ( w h i c h a r e a d i r e c t f u n c t i o n o f p r e v i o u s s t a r t s ) . The l a c k o f r e l i a b l e , c o n s i s t e n t d a t a d i c t a t e d t h a t M a i s e l ' s h o u s i n g s t a r t s e q u a t i o n be e s t i m a t e d u s i n g a r e d u c e d f o r m e q u a t i o n w i t h i n t e r e s t r a t e s , d e v i a t i o n s i n v a c a n c y r a t e s f r o m t h e t r e n d , l a g g e d s t a r t s , t h e r a t i o o f r e n t s t o r e s i d e n t i a l c o s t s , e s t i m a t e d r e m o v a l s and t h e c h a n g e i n t h e number o f h o u s e h o l d s . B a s e d on q u a r t e r l y d a t a f r o m 1950 t o 1960, t h e e s t i m a t e d e q u a t i o n y i e l d e d an R 2 o f .878. The c o n c e p t u a l i z a t i o n o f M a i s e l ' s model a p p e a r s s o u n d , b u t d i f f i c u l t i e s a r i s e i n t h e e m p i r i c a l d e v e l o p m e n t . The most s e v e r e c r i t i c i s m i s t h e e s t i m a t i o n o f t h e r e m o v a l s s e r i e s ; c a l c u l a t e d a s t h e r e s i d u a l o f t h e c h a n g e i n s t o c k n o t a c c o u n t e d f o r by new s t a r t s . C o n s e q u e n t l y , t h e h i g h R 2 .and s i g n i f i c a n c e o f t h i s v a r i a b l e c o u l d be e x p e c t e d . A l s o , u s i n g n a t i o n a l d a t a i g n o r e s t h e l o c a l i z e d n a t u r e o f t h e h o u s i n g m a r k e t . R e s i d e n t i a l c o n s t r u c t i o n w i l l be d e p e n d e n t upon l o c a l e c o n o m i c c o n d i t i o n s a n d e x p e c t a t i o n s . When some a r e a s a r e e x p e r i e n c i n g l o w e r c o n s t r u c t i o n , o t h e r a r e a s may be n o t i n g h i g h e r l e v e l s o f c o n s t r u c t i o n a c t i v i t y . C o n s e q u e n t l y , by a g g r e g a t i o n o f t h e s e d a t a , n a t i o n a l r e s u l t s w i l l n o t f u l l y r e f l e c t t h e r e s p o n s i v e n e s s of r e s i d e n t i a l c o n s t r u c t i o n . 2.3.2 S m i t h - B i - S e c t o r a l H o u s i n g M o d e l The h o u s i n g m a r k e t c a n be d e s c r i b e d a s a s e r i e s o f o v e r l a p p i n g s u b m a r k e t s b a s e d on l o c a t i o n , d w e l l i n g t y p e , t e n u r e , 1 7 age and q u a l i t y . S m i t h a t t e m p t s t o d i s a g g r e g a t e t h e s i n g l e f a m i l y and m u l t i f a m i l y m a r k e t s by d e v e l o p i n g , a b i - s e c t o r a l m o d e l w h i c h i n v e s t i g a t e s t h e d i f f e r e n c e s b e t w e e n t h e s e two s e c t o r s . H i s p r e m i s e f o r t h i s d i s t i n c t i o n i s t h e c h a n g i n g p r o p o r t i o n s o f s t a r t s i n e a c h s e c t o r and t h e v e r y d i f f e r e n t r a t e s o f c h a n g e i n r e n t s and h o u s e p r i c e s b e t w e e n 1951 and 1967 ( 1 9 6 9 , p 5 5 9 ) . The o v e r a l l m o d e l d e v e l o p e d i s a " s t o c k - f l o w m o d e l i n w h i c h t h e v o l u m e o f h o u s i n g s t a r t s d e p e n d s upon a c o m p a r i s o n o f h o u s e p r i c e s o r r e n t s and v a c a n c y r a t e s w i t h c o n s t r u c t i o n , l a n d and f i n a n c i n g c o s t s , and t h e a v a i l a b i l i t y o f p u b l i c a n d p r i v a t e m o r t g a g e c r e d i t . P r i c e s , r e n t s and v a c a n c y r a t e s a r e d e t e r m i n e d by t h e demand f o r and s u p p l y o f e a c h t y p e o f h o u s i n g a c c o m o d a t i o n . The demand f o r s i n g l e u n i t d w e l l i n g s d e p e n d s upon t h e p r i c e a n d c a r r y i n g c o s t s o f t h i s f o r m o f a c c o m o d a t i o n a n d t h e p r i c e o f n o n - h o u s i n g g o o d s and s e r v i c e s , p e r m a n e n t r e a l d i s p o s a b l e i n c o m e , d e m o g r a p h i c f a c t o r s , and t h e c o s t s and a v a i l a b i l i t y o f m o r t g a g e c r e d i t . " ( 1 9 6 9 , p 5 5 9 ) The e q u a t i o n s p r e s e n t e d f o r t h e l e v e l o f s t a r t s i n e a c h s e c t o r a r e e s s e n t i a l l y t h e same, w i t h t h e p r i c e o f h o u s i n g and t h e s i n g l e f a m i l y s t o c k e n t e r i n g t h e s i n g l e s t a r t s e q u a t i o n , and r e n t s and t h e m u l t i f a m i l y s t o c k b e i n g u s e d f o r t h e m u l t i f a m i l y s t a r t s e q u a t i o n . M u l t i f a m i l y s t a r t s a r e g i v e n a s a f u n c t i o n o f r e n t s , v a c a n c y r a t e s i n m u l t i d w e l l i n g s t r u c t u r e s , c o n s t r u c t i o n c o s t s , l a n d c o s t s , t h e c o s t o f c r e d i t , t h e a v a i l a b i l i t y o f p r i v a t e m o r t g a g e f u n d s a n d t h e c o s t s a n d a v a i l a b i l i t y o f p u b l i c (CMHC) m o r t g a g e f u n d s . Some o f t h e v a r i a b l e s were e l i m i n a t e d f r o m t h e e s t i m a t e d 18 r e g r e s s i o n s , o r p r o x y v a r i a b l e s d e r i v e d , s i n c e t h e d a t a s e r i e s a v a i l a b l e f o r e s t i m a t i n g t h e e q u a t i o n s were e i t h e r o f p o o r q u a l i t y o r u n a v a i l a b l e . D u r i n g t h e p e r i o d u n d e r i n v e s t i g a t i o n , 1954 t o 1965, t h e r e was no r e l i a b l e v a c a n c y r a t e s e r i e s . E l i m i n a t i o n o f v a c a n c y r a t e s f r o m t h e e m p i r i c a l r e s u l t s i m p l i e s t h a t m a r k e t c o n d i t i o n s a r e f u l l y r e p r e s e n t e d i n h o u s e p r i c e s and r e n t s . The d i f f e r e n c e b e t ween m o r t g a g e r a t e s and bond y i e l d s was u s e d a s a p r o x y f o r t h e a v a i l a b i l i t y o f m o r t g a g e c r e d i t . F i n a l l y , a dummy v a r i a b l e was u s e d f o r t h e g o v e r n m e n t w i n t e r b u i l d i n g p r o g r a m w h i c h was i n e f f e c t f r o m 1963 t o 1966. The r e s u l t s y i e l d an R 2 o f 0.89 f o r t h e m u l t i p l e d w e l l i n g s t a r t s e q u a t i o n and 0.93 f o r t h e s i n g l e s t a r t s e q u a t i o n . The m a i n d i s t i n c t i o n f o r t h e two s e c t o r s i s i n t h e c o s t and a v a i l a b i l i t y o f c r e d i t . The c o s t o f c r e d i t c o e f f i c i e n t i s s i m i l a r a n d s i g n i f i c a n t f o r b o t h s e c t o r s , b u t t h e p r o x y f o r t h e a v a i l a b i l i t y o f c r e d i t was s i g n i f i c a n t o n l y i n t h e s i n g l e f a m i l y s e c t o r . From t h i s S m i t h c o n c l u d e s t h a t d e v e l o p e r s o f m u l t i u n i t p r o j e c t s w i l l be more s e n s i t i v e t o t h e c o s t o f c r e d i t , o r i n t e r e s t r a t e s w h i c h a f f e c t p r o f i t a b i l i t y t h a n t o n o n - p r i c e t e r m s . T h i s i s s u p p o r t e d by t h e g r e a t e r w i l l i n g n e s s o f f i n a n c i a l i n s t i t u t i o n s t o l e n d t o " l a r g e c o r p o r a t e b o r r o w e r s who d o m i n a t e t h e m u l t i p l e d w e l l i n g c o n s t r u c t i o n r a t h e r t h a n s m a l l e r b u i l d e r s who a r e p r e v e l a n t i n t h e c o n s t r u c t i o n o f s i n g l e u n i t d w e l l i n g s " . ( p 5 6 3 ) O t h e r v a r i a b l e s i n t h e e q u a t i o n s u p p p o r t e d t h e h y p o t h e s i s t h a t t h e two m a r k e t s e g m e n t s a r e d i s t i n c t . H i g h e r l a n d c o s t s i n c r e a s e t h e number o f m u l t i p l e s t a r t s and d e c r e a s e t h e number 19 o f s i n g l e s t a r t s . T h i s c h a n g e o f s i g n was e x p e c t e d on t h e b a s i s m a x i m i z i n g l a n d u se a s l a n d c o s t s i n c r e a s e . The r a t i o o f r e n t s t o c o n s t r u c t i o n c o s t s i s more s i g n i f i c a n t t h a n t h e r a t i o o f h o u s i n g p r i c e s t o c o n s t r u c t i o n c o s t s . S m i t h s u g g e s t s t h i s may be t h e i m p a c t o f c u s t o m h o u s e c o n s t r u c t i o n i n t h e s i n g l e s e c t o r and s p e c u l a t i v e b u i l d i n g i n t h e r e n t a l s e c t o r . To c o m p l e t e t h e m o d e l , S m i t h t h e n d e r i v e s e q u a t i o n s f o r t h e demand f o r s i n g l e a n d m u l t i p l e u n i t s , t h e r e l a t i v e p r i c e s and t h e t o t a l s u p p l y o f u n i t s i n e a c h m a r k e t s e c t o r . T h e s e f u r t h e r s u p p o r t h i s h y p o t h e s i s o f d i s t i n c t m a r k e t s . By d e v e l o p i n g s i m i l a r e q u a t i o n s f o r e a c h m a r k e t s e g m e n t , S m i t h d o e s n o t a d d r e s s t h e p o s s i b i l i t y o f demand o r s u p p l y i n f l u e n c e s b e i n g d i f f e r e n t f o r e i t h e r m a r k e t . The model w o u l d s u g g e s t t h a t b o t h m a r k e t s a r e s u p p l y d r i v e n w h i c h i s i n c o n t r a s t t o o t h e r s t u d i e s . 2.3.3 J a f f e e & Rosen - C r e d i t A v a i l a b i l i t y & R e s i d e n t i a l C o n s t r u c t i o n J a f f e e a n d Rosen d e v e l o p a n a t i o n a l m o d e l f o r t h e h o u s i n g , m o r t g a g e and d e p o s i t s e c t o r s o f t h e economy b a s e d on f i v e e q u a t i o n s ; t h e s t o c k - l e v e l demand f o r home o w n e r s h i p , s i n g l e f a m i l y h o u s i n g s t a r t s , m u l t i f a m i l y h o u s i n g s t a r t s , t h e i n t e r e s t r a t e on m o r t g a g e s and t h e d e p o s i t f l o w s o f t h r i f t i n s t i t u t i o n s . Of s p e c i a l s i g n i f i c a n c e i s t h e e x p l i c i t m o d e l l i n g o f d e m o g r a p h i c c h a n g e and t h e d e v e l o p m e n t o f s e p a r a t e e q u a t i o n s f o r t h e s i n g l e and m u l t i f a m i l y h o u s i n g m a r k e t s . The s t o c k - l e v e l demand f o r h o u s i n g i s e s t i m a t e d b a s e d on t h e d e m o g r a p h i c c o m p o s i t i o n o f t h e p o p u l a t i o n a n d t h e h e a d s h i p 20 r a t e s f o r e a c h age c o h o r t . J a f f e e a n d R o s e n p r o p o s e t h a t t h e a c t u a l p o p u l a t i o n a n d age d i s t r i b u t i o n a r e g e n e r a l l y known. The t r a n s f o r m a t i o n o f t h i s d a t a i n t o h o u s e h o l d u n i t s c o n t a i n s some u n c e r t a i n t y , b u t i s f a i r l y p r e d i c t a b l e i n t h e s h o r t r u n . By a s s u m i n g c o n s t a n t h e a d s h i p r a t e s f o r o w n e r - o c c u p i e d h o u s i n g o v e r t h e e s t i m a t i o n p e r i o d , t h e number o f h o u s e h o l d s c a n be p r o j e c t e d . The r a t i o o f t h e a c t u a l number o f h o u s e h o l d s t o t h i s a d j u s t e d number o f h o u s e h o l d s p r o v i d e s an i n d i c a t o r o f h o u s e h o l d f o r m a t i o n w h i c h c a n n o t be a t t r i b u t e d t o d e m o g r a p h i c c h a n g e a n d , t h e r e f o r e , must be t h e r e s u l t o f c h a n g i n g e c o n o m i c c o n d i t i o n s . T h i s e s t i m a t i o n p r o c e d u r e i s o n l y u s e d f o r t h e s i n g l e f a m i l y h o u s i n g m a r k e t . J a f f e e a nd Rosen s t a t e t h a t i n t h e s i n g l e f a m i l y m a r k e t , c o n s t r u c t i o n i s d e t e r m i n e d by t h e demand s i d e v a r i a b l e s . The e q u a t i o n f o r t h e c h a n g e i n t h e number o f o w n e r s i n c l u d e s f o u r e c o n o m i c v a r i a b l e s : t h e r a t i o o f o w n e r s h i p c o s t s t o r e n t a l c o s t s , t h e unemployment r a t e a nd 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 , t o g e t h e r w i t h t h e p r e v i o u s 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 . The a d j u s t e d number o f h o u s e h o l d s i s u s e d a s a m u l t i p l i c a t i v e f a c t o r i n t h i s e q u a t i o n s o t h a t t h e c o e f f i c i e n t s o f t h e e c o n o m i c v a r i a b l e s w i l l r e f l e c t o n l y n o n - d e m o g r a p h i c s h i f t s . S i n g l e u n i t s t a r t s a r e t h e n g i v e n a s a f u n c t i o n o f t h e c h a n g e i n t h e number o f o w n e r - o c c u p i e d h o u s i n g u n i t s , t h e e x i s t i n g s t o c k , t h e number o f v a c a n t u n i t s a nd m o r t g a g e c r e d i t a v a i l a b i l i t y a n d c o s t s . I n t h e e s t i m a t i o n o f t h i s s t a r t s e q u a t i o n , t h e f i t t e d c h a n g e i n t h e number o f o w n e r s i s u s e d f o r t h e a c t u a l c h a n g e i n t h e number o f o w n e r - o c c u p i e d h o u s i n g u n i t s . 21 J a f f e e a n d Rosen f o l l o w t h e g e n e r a l c o n c e n s u s a n d assume t h a t t h e m u l t i f a m i l y c o n s t r u c t i o n i s d e t e r m i n e d by s u p p l y s i d e v a r i a b l e s and p r o f i t m a x i m i z a t i o n o f t h e m a r k e t p a r t i c i p a n t s . F i v e f a c t o r s a r e t h e n p r o p o s e d f o r t h e m u l t i u n i t s t a r t s e q u a t i o n : p r o f i t m a r g i n s , m o r t g a g e i n t e r e s t r a t e s , m u l t i f a m i l y v a c a n c y r a t e s , m o r t g a g e f u n d r a t i o n i n g a n d t h e s t o c k o f m u l t i f a m i l y u n i t s ( u s e d a s a s c a l i n g f a c t o r ) . U s i n g U.S. n a t i o n a l d a t a , q u a r t e r l y f r o m 1964:1 t o 1978:2, t h e e s t i m a t i o n y i e l d e d an R 2 o f 0.944 w i t h a l l v a r i a b l e s s i g n i f i c a n t . The f i n a l e q u a t i o n i n c l u d e d p r o f i t ( e s t i m a t e d a s t h e r e n t a l C P l d e f l a t e d by t h e t o t a l C P l ) , r e a l i n t e r e s t r a t e s and t h e c h a n g e i n d e p o s i t s t o t h r i f t i n s t i t u t i o n s d e f l a t e d by t h e t o t a l C P l was a s a p r o x y f o r m o r t g a g e f u n d r a t i o n i n g . The n e x t s t a g e o f t h e m o d e l i s an e s t i m a t i o n f o r m o r t g a g e i n t e r e s t r a t e s b a s e d on t h e s u p p l y a n d demand f o r m o r t g a g e f u n d s . F i n a l l y , t h e f l o w o f f u n d s t o t h r i f t i n s t i t u t i o n s i s e s t i m a t e d u s i n g i n t e r e s t r a t e s a n d r a t e s o f p e r s o n a l s a v i n g s . The d i f f e r e n c e s i n t h e C a n a d i a n a n d U.S. m o r t g a g e m a r k e t s r e d u c e t h e a p p l i c a b i l i t y o f t h e s e f u r t h e r m o d e l d e r i v a t i o n s . W i t h r e s p e c t t o t h e m u l t i f a m i l y m a r k e t s , J a f f e e a n d Rosen c o n c l u d e t h a t c o n s t r u c t i o n i s d e t e r m i n e d by t h e s u p p l y s i d e p r o f i t i n c e n t i v e s f o r b u i l d e r s . A l t h o u g h t h e y e x p l i c i t l y m odel t h e n o n - d e m o g r a p h i c demand f o r s i n g l e f a m i l y u n i t s , t h e y i g n o r e t h i s component i n t h e m u l t i f a m i l y s e c t o r , on t h e a s s u m p t i o n t h a t c o n s t r u c t i o n i n t h e m u l t i f a m i l y h o u s i n g m a r k e t i s s u p p l y o r i e n t e d and t h e r e f o r e t h e m a r k e t demand i s r e f l e c t e d i n v a c a n c y r a t e s and p r i c e s ( r e n t s ) . F i n a l l y , a l t h o u g h t h e r e s u l t s o f t h e 22 e s t i m a t e s a r e s i g n i f i c a n t , r e g i o n a l i m p a c t s c a n n o t be d e t e r m i n e d f r o m t h e n a t i o n a l r e s u l t s d e r i v e d . 2.3.4 Rosen - R e g i o n a l M o d e l o f M u l t i , F a m i l y H o u s i n g S t a r t s R o s e n p r o p o s e s t h a t t h e e x t r e m e v o l a t i l i t y i n m u l t i f a m i l y h o u s i n g c o n s t r u c t i o n i s t h e r e s u l t o f i n v e n t o r i e s a c c u m u l a t i n g u n t i l t h e r e i s a s h a r p r e d u c t i o n i n s t a r t s t o p e r m i t t h e a d d i t i o n a l u n i t s t o be a b s o r b e d . T h i s i s b a s e d on t h e a s s u m p t i o n o f t h e d i s e q u i l i b r i u m p r o c e s s , w h e r e b y v a c a n c i e s a d j u s t q u i c k l y t o c h a n g e s i n t h e m a r k e t , b u t r e n t a l p r i c e s and t h e s t o c k r e s p o n d more s l o w l y . E s s e n t i a l l y , t h e f i r s t r e s p o n s e i n t h e m a r k e t t o an i n c r e a s e ( d e c r e a s e ) i n demand w i l l be r e f l e c t e d i n v a c a n c i e s , t h e n , w i t h a l a g , r e n t a l p r i c e s s h o u l d a d j u s t t o r e f l e c t t h e i n c r e a s e ( d e c r e a s e ) i n demand. F i n a l l y , new c o n s t r u c t i o n and c o n v e r s i o n s s h o u l d be u n d e r t a k e n ( d e l a y e d o r a b a n d o n e d ) . G i v e n t h i s o v e r v i e w o f m a r k e t o p e r a t i o n s , R o s e n s t a t e s t h a t t h e s u p p l y o f m u l t i f a m i l y u n i t s w i l l be d e p e n d e n t upon t h e p r o f i t m a x i m i z a t i o n d e c i s i o n s o f e x i s t i n g l a n d l o r d s and new p o t e n t i a l i n v e s t o r s . P r o f i t i n c l u d e s e x p e c t e d r e v e n u e s , t h e o c c u p a n c y r a t e , o c c u p a n c y c o s t s , c o n s t r u c t i o n a n d l a n d c o s t s , d e p r e c i a t i o n t a x b e n e f i t s a n d c a p i t a l g a i n s . F o r t h e e m p i r i c a l a n a l y s i s , t h e U.S. i s d i v i d e d i n t o f o u r r e g i o n s ( N o r t h e a s t , N o r t h C e n t r a l , S o u t h , W e s t ) and l o g g e d e q u a t i o n e s t i m a t e d f o r h o u s i n g s t a r t s i n e a c h r e g i o n . The r e s u l t s i n d i c a t e d i s t i n c t r e g i o n a l d i f f e r e n c e s and e m p h a s i s t h e i m p o r t a n c e o f p r o f i t a b i l i t y . P r o f i t a b i l i t y i s e s t i m a t e d a s t h e 23 r e n t a l component o f t h e C P l d e f l a t e d by t h e t o t a l C P l . The e l a s t i c i t y o f t h i s v a r i a b l e r a n g e d f r o m 5.69 ( N o r t h C e n t r a l ) t o 14.31 ( S o u t h ) . The r e g r e s s i o n r e s u l t s f o r t h e s e e q u a t i o n s a r e s i g n i f i c a n t , b u t , R o s en n o t e s t h a t t h e r e s u l t s do n o t y e t i n c l u d e t h e demand s i d e o f t h e m a r k e t , n o r t h e i m p a c t o f t a x e s a n d g o v e r n m e n t p o l i c y . T h e s e a r e p r o p o s e d f o r f u t u r e s t u d y . A f u r t h e r c r i t i c i s m i s i n t h e a s s u m p t i o n t h a t v a c a n c y r a t e s w i l l r e f l e c t a l l a v a i l a b l e i n v e n t o r y . T h i s i g n o r e s n e w l y c o m p l e t e d u n i t s w h i c h have n o t y e t been i n c l u d e d i n t h e s t o c k s u r v e y f o r v a c a n c i e s . A l t h o u g h t h e b e n e f i t s o f r e g i o n a l r e s u l t s a r e e v i d e n t , t h e r e g i o n s c h o s e n may s t i l l be t o o l a r g e t o " r e f l e c t t h e h o u s i n g m a r k e t a c c u r a t e l y . W i t h i n e a c h o f t h e f o u r r e g i o n s d e f i n e d , t h e r e c o u l d be v e r y d i v e r s e m a r k e t t r e n d s w h i c h w i l l i n f l u e n c e t h e f i n a l r e s u l t s . 2.4 COMMENTS ON EXISTING WORK E x a m i n a t i o n o f t h e e x i s t i n g l i t e r a t u r e on h o u s i n g m a r k e t s and more s p e c i f i c a l l y h o u s i n g s t a r t s i n d i c a t e s some c o n c e n s u s on t h e n a t u r e o f t h e m a r k e t , b u t a l s o r a i s e s s e v e r a l i s s u e s . W i t h some d e v i a t i o n s , t h e demand f o r h o u s i n g u n i t s , o r t h e r a t e o f h o u s e h o l d f o r m a t i o n i s g e n e r a l l y g i v e n a s a f u n c t i o n o f i n c o m e , unemployment r a t e s , t h e p r i c e o f h o u s i n g ( r e n t s a n d / o r o w n e r s h i p c o s t s ) a n d t h e p r i c e o f o t h e r g o o d s and s e r v i c e s . Where t h e s u p p l y o f r e n t a l a n d o w n e r - o c c u p i e d h o u s i n g u n i t s a r e s e g r e g a t e d , t h e s u p p l y o f s i n g l e u n i t s i s assumed t o r e s p o n d t o demand v a r i a t i o n s . A l t e r n a t i v e l y , m u l t i d w e l l i n g c o n s t r u c t i o n 24 i s t h o u g h t t o be s u p p l y o r i e n t e d ; r e s p o n d i n g t o p r o f i t m a x i m i z a t i o n , v a c a n c i e s a n d i n t e r e s t r a t e s . T h e s e v a r i a b l e s seem, t o be t h e key c o m p o n e n t s i n t h e t h e o r e t i c a l m o d e l s , b u t , t h e r e i s no c o n c e n s u s on t h e e s t i m a t i o n t e c h n i q u e s o r r e s u l t s . Some o f t h e key i s s u e s w h i c h r a i s e q u e s t i o n s i n t h e e x i s t i n g l i t e r a t u r e , o r r e q u i r e f u r t h e r i n v e s t i g a t i o n i n c l u d e : 1. The e x i s t i n g r e s e a r c h on h o u s i n g s t a r t s h a s f o c u s e d on t h e i m p a c t o f c r e d i t c o s t s and a v a i l a b i l i t y . E v i d e n c e s u g g e s t s t h a t t h e c o s t o f c r e d i t may be i m p o r t a n t , b u t n o t n e c e s s a r i l y t h e p r i m a r y c o n s i d e r a t i o n . D i f f i c u l t y i n t h i s r e g a r d i s c o m p l i c a t e d by t h e d i f f e r e n c e s o f C a n a d i a n a n d U.S. m o r t g a g e m a r k e t s a n d t h e l i m i t e d r e s e a r c h i n t h e C a n a d i a n m a r k e t . 2. M o s t o f t h e a n a l y s i s h ave been b a s e d on n a t i o n a l s t a r t s d a t a . S i n c e h o u s i n g i s an i m m o b i l e a n d d u r a b l e g o o d , t h e r e w i l l be r e g i o n a l d i f f e r e n c e s i n m a r k e t c o n d i t i o n s a n d a c t i v i t i e s . By i g n o r i n g t h e s e s u b m a r k e t s , i n f o r m a t i o n on t h e i m p a c t o f r e g i o n a l e c o n o m i c c o n d i t i o n s w i l l n o t be c o n s i d e r e d . 3. The i m p o r t a n c e o f t h e d e m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n on f u t u r e demand i s n o t e d i n most o f t h e p r e v i o u s work. T h e r e a r e few a t t e m p t s , h o w e v e r , t o e s t i m a t e t h e i m p o r t a n c e o f t h i s demand, o r c h a n g e s i n t h e e x p e c t e d demand on t h e s u p p l y o f h o u s i n g u n i t s . 4. More r e c e n t s t u d i e s h a v e r e c o g n i z e d t h e d i s t i n c t i o n between- t h e s i n g l e a n d m u l t i d w e l l i n g u n i t 25 m a r k e t s . However, most m o d e l s a r e s t i l l b a s e d on t h e t o t a l h o u s i n g m a r k e t , i m p l i c i t l y a s s u m i n g t h a t t h e ^ s u b m a r k e t s a r e r e s p o n d i n g t o s i m i l a r s t i m u l i . Of g r e a t e r i m p o r t a n c e i s t h e n e e d t o r e c o g n i z e t h e s u b s t i t u t a b i l i t y o f t h e s h e l t e r component o f r e n t a l o r o w n e r - o c c u p i e d h o u s i n g and t h e a d d e d i n v e s t m e n t component o f h o m e o w n e r s h i p . 5. The n e e d f o r g o v e r n m e n t i n t e r v e n t i o n i n r e n t a l m a r k e t s h a s been d i s c u s s e d i n some p a p e r s , b u t a s y e t , t h e i m p a c t s f o g o v e r n m e n t and t a x p o l i c y on t h e h o u s i n g m a r k e t r e m a i n u n c e r t a i n and c o n t r o v e r s i a l . 6. T h e r e i s a l a c k o f . r e l i a b l e a nd c o n s i s t e n t d a t a on t h e h o u s i n g m a r k e t . C o n s e q u e n t l y , many m o d e l s r e l y on p r o x y m e a s u r e s and e s t i m a t e d s e r i e s . T h i s h a s s e v e r e l y r e d u c e d t h e v a l i d i t y o f r e s u l t s . 7. The l i n k b e t w een t h e demand f o r and s u p p l y o f h o u s i n g u n i t s h a s n o t been f u l l y e x p l o r e d . T h e r e i s l i t t l e d i s c u s s i o n o f t h e u s e o f i n v e n t o r y l e v e l s a s a b u f f e r b e t w e e n t h e m a r k e t p a r t i c i p a n t s a nd u n e x p e c t e d e v e n t s i n t h e m a r k e t . I n a d d i t i o n t o t h e s e p r o b l e m s w i t h t h e o v e r a l l r e s e a r c h on h o u s i n g s t a r t s , t h e r e i s v e r y l i t t l e r e s e a r c h r e l a t i n g t o t h e C a n a d i a n m a r k e t . S i n c e C a n a d i a n m o r t g a g e m a r k e t s , t a x l a w s , g o v e r n m e n t p o l i c y a n d p e r h a p s h o u s i n g c o n s u m p t i o n p a t t e r n s a r e d i f f e r e n t t h a n t h o s e f o u n d i n U.S. c i t i e s , i t w o u l d be r e a s o n a b l e t o a n t i c i p a t e d i f f e r e n t e m p i r i c a l r e s u l t s . 26 3. IMPACTS OF GOVERNMENT PROGRAMS AND POLICY The p r o p o s e d m o d e l i s b a s e d on t h e a s s u m p t i o n o f a c o m p e t i t i v e h o u s i n g m a r k e t w i t h no g o v e r n m e n t p r o g r a m s o r p o l i c i e s t o i n f l u e n c e i n v e s t m e n t i n t h e r e n t a l m a r k e t o r t h e a t t r a c t i v e n e s s o f home o w n e r s h i p . T h i s i d e a l i s t i c s c e n a r i o d o e s n o t a c c u r a t e l y r e f l e c t t h e s t a t e o f t h e p o s t - w a r C a n a d i a n h o u s i n g m a r k e t . G o v e r n m e n t i n t e r v e n t i o n h a s had a s i g n i f i c a n t i m p a c t on t h e h o u s i n g m a r k e t , t h e r e f o r e , an u n d e r s t a n d i n g o f t h e s e p o l i c i e s i s a p r e r e q u i s i t e t o any d i s c u s s i o n o f t h e m a r k e t s t r u c t u r e o r f o r e c a s t i n g m o d e l . D e s p i t e some p r o g r a m s s p e c i f i c a l l y d e s i g n e d t o e n c o u r a g e i n v e s t m e n t i n t h e r e n t a l m a r k e t , t h e g e n e r a l b i a s o f F e d e r a l h o u s i n g p o l i c y h a s been t o w a r d h o m e o w n e r s h i p . P o l i c i e s i n t h e P r o v i n c e o f B r i t i s h C o l u m b i a h a v e e c h o e d t h i s b i a s . The f o l l o w i n g p r o v i d e s a b r i e f o v e r v i e w o f t h e p o l i c i e s a n d p r o g r a m s i n f l u e n c i n g t h e V a n c o u v e r m u l t i f a m i l y h o u s i n g m a r k e t d u r i n g t h e s t u d y p e r i o d . I t i s b e y o n d t h e s c o p e o f t h i s p a p e r t o d i s c u s s t h e s e p r o g r a m s a nd t h e i r i m p a c t s i n any d e t a i l . Comments t h e r e f o r e , a r e l i m i t e d t o t h e i m p l i c a t i o n s f o r t h e p r o p o s e d t h e o r e t i c a l a n d e m p i r i c a l a n a l y s i s . 5 3.1 GENERAL POLICY CHANGES: (a) S t r a t a T i t l e s I n B r i t i s h C o l u m b i a i n 1966, l e g i s l a t i o n was p a s s e d p e r m i t t i n g t h e r e g i s t r a t i o n o f s t r a t a t i t l e s , o w n e r s h i p o f 27 i n d i v i d u a l u n i t s w i t h i n a m u l t i - u n i t s t r u c t u r e . F u r t h e r l e g i s l a t i o n i n 1974 r e s t r i c t e d t h e c o n v e r s i o n o f e x i s t i n g r e n t a l b u i l d i n g s t o c o n d o m i n i u m s by r e q u i r i n g a p p r o v a l f r o m a t l e a s t 90 p e r c e n t o f t h e e x i s t i n g t e n a n t s . The a b i l i t y t o own a u n i t i n a m u l t i - u n i t d w e l l i n g c l e a r l y a f f e c t s t h e m u l t i f a m i l y h o u s i n g m a r k e t , i n v a l i d a t i n g t h e common a s s u m p t i o n t h a t m u l t i f a m i l y u n i t s a r e a u t o m a t i c a l l y r e n t a l u n i t s . E s t i m a t i o n s o f t h e e x i s t i n g m u l t i p l e s t o c k must d i s t i n g u i s h b e t w e e n o w n e r - o c c u p i e d an d r e n t a l u n i t s . New c o n s t r u c t i o n may be f o r e i t h e r m a r k e t . B u i l d i n g s c a n be r e g i s t e r e d a s a c o n d o m i n i u m s , b u t a c t u a l l y end up b e i n g r e n t e d upon c o m p l e t i o n . The d e v e l o p m e n t o f t h e c o n d o m i n i u m m a r k e t i n t h e V a n c o u v e r a r e a c r e a t e s d i f f i c u l t i e s i n a n a l y s i n g t h e a v a i l a b l e c o n s t r u c t i o n d a t a a n d t r y i n g t o d e t e r m i n e t h e s i z e o f t h e r e n t a l m a r k e t . 3.2 DEMAND ORIENTED P O L I C I E S (a) P r o v i n c i a l Home Owner G r a n t A c t P a s s e d i n 1957, t h i s a c t p r o v i d e d a f i x e d a n n u a l g r a n t t o a l l homeowners i n B r i t i s h C o l u m b i a . D i s t r i b u t i o n was t h r o u g h m u n i c i p a l t a x e s , where t h e g r a n t was a p p l i e d t o t h e r e s i d e n t ' s t a x e s up t o t h e l e s s e r o f t h e maximum g r a n t o r t o t a l p r o p e r t y t a x e s . I n i t i a l l y , o n l y s i n g l e - d e t a c h e d a n d d u p l e x u n i t s q u a l i f i e d ; h o w e v e r , i n 1960 t h i s was amended t o i n c l u d e any p r o p e r t y where t h e owner i s r e s i d e n t . 6 The maximum g r a n t r o s e f r o m $28 i n 1957 t o $200 i n 1973. 28 (b) Home A c q u i s i t i o n P r o g r a m T h i s p r o g r a m , s t a r t e d i n A p r i l 1966, p r o v i d e d p u r c h a s e r s o f new and e x i s t i n g d w e l l i n g s who had r e s i d e d i n B r i t i s h C o l u m b i a f o r a t l e a s t one y e a r , a g r a n t o f $500. I n A p r i l 1967 t h e g r a n t was i n c r e a s e d t o $525 w i t h t h e i n t e n t o f a n n u a l i n c r e a s e s o f $25. The p r o g r a m u n d e r w e n t c h a n g e s and i n 1976 p u r c h a s e r s o f new h o u s i n g u n i t s were e l i g i b l e f o r a $1000 b u i l d i n g o r a c q u i s i t i o n g r a n t o r a $5000 s e c o n d m o r t g a g e . P u r c h a s e r s o f e x i s t i n g h o u s e s were e l i g i b l e f o r a $500 a c q u i s i t i o n g r a n t , o r a $2500 s e c o n d m o r t g a g e . The s e c o n d mortgage- c o u l d be a p p l i e d t o t h e downpayment, e x c e p t where t h e f i r s t m o r t g a g e was NHA i n s u r e d . 7 A t t h e t i m e t h i s p r o g r a m was c a n c e l l e d i n J u l y 1983, g r a n t s o f $1000 were a v a i l a b l e f o r s i n g l e h o u s e h o l d s and o f $2500 f o r h o u s e h o l d s w i t h a t l e a s t one d e p e n d e n t l e s s t h a n 19 y e a r s o f a g e . ( c ) R e n t e r s ' R e s o u r c e G r a n t A c t To o f f s e t t h e b e n e f i t s t o homeowners, t h e P r o v i n c i a l G o v ernment o f B r i t i s h C o l u m b i a p a s s e d t h e R e n t e r ' s R e s o u r c e G r a n t A c t i n 1974. G r a n t s of $30 p e r annum were a v a i l a b l e t o a l l r e n t e r s who a p p l i e d , w i t h an a d d i t i o n a l $50 t o t h o s e o v e r 65. D i s t r i b u t i o n c h a n g e d i n 1976; f o r m s were i n c l u d e d w i t h i ncome t a x r e t u r n s , income l i m i t a t i o n s were i m p o s e d and r e b a t e s i n c r e a s e d (up t o $100, d e p e n d i n g on t h e income o f t h e a p p l i c a n t ) . T h i s p r o g r a m c e a s e d w i t h t h e f i l i n g o f 1982 t a x r e t u r n s . • 29 (d) G r a n t t o New Home B u y e r s From November 1974 t o O c t o b e r 1975 t h e F e d e r a l G o v e r n m e n t p r o v i d e d a g r a n t o f $500 t o f i r s t t i m e home b u y e r s . To q u a l i f y , t h e u n i t s p u r c h a s e d h a d t o be n e w l y c o n s t r u c t e d a n d p r i c e d b e l o w a s e t l i m i t . L i m i t s were s e t by CMHC a c c o r d i n g t o a v e r a g e h o u s e p r i c e s i n e a c h r e g i o n . ( e ) A s s i s t e d Home O w n e r s h i p P r o g r a m (AHOP) The o b j e c t i v e o f t h i s p r o g r a m was t o e n a b l e l o w e r income f a m i l i e s t o own h o u s e s w i t h o u t s p e n d i n g o v e r 25 p e r c e n t o f t h e i r i ncome on s h e l t e r . M o r t g a g e s were p r o v i d e d by CMHC a t f a v o u r a b l e i n t e r e s t r a t e s a n d w i t h h i g h l o a n - t o - v a l u e r a t i o s . A m o r t g a g e s u b s i d y o f up t o $1200 p e r y e a r was a v a i l a b l e t o o f f s e t t h e m o r t g a g e c o s t s . The AHOP p r o g r a m , a d m i n i s t e r e d by t h e F e d e r a l G o v e r n m e n t was i n e f f e c t f r o m 1973 t o 1978. 3.2 SUPPLY ORIENTED P O L I C I E S ( a ) W i n t e r House B u i l d i n g P r o g r a m I n p l a c e f r o m 1963 t o t h e s p r i n g o f 1966, t h e W i n t e r House B u i l d i n g P r o g r a m p r o v i d e d a s u b s i d y o f $500 p e r d w e l l i n g s u b s t a n t i a l l y c o n s t r u c t e d b e t w e e n December 1 and M a r c h 31 e a c h y e a r . T h i s was a v a i l a b l e o n l y f o r s t r u c t u r e s o f 1 t o 4 d w e l l i n g s , e l i m i n a t i n g most m u l t i f a m i l y d w e l l i n g s . C o n s e q u e n t l y , i t w o u l d be e x p e c t e d t h a t s i n g l e f a m i l y c o n s t r u c t i o n w o u l d be s h i f t e d t o t h e f o u r t h q u a r t e r t o b e n e f i t f r o m t h i s p r o g r a m , w h i l e m u l t i p l e u n i t c o n s t r u c t i o n may s u b s e q u e n t l y be s h i f t e d t o o t h e r q u a r t e r s . 30 (b) NHA M u l t i - u n i t L o a n s The N a t i o n a l H o u s i n g A c t r e s t r i c t e d t h e l e v e l o f i n t e r e s t r a t e s , l o a n - t o - l e n d i n g v a l u e r a t i o s and t h e maximum l o a n a v a i l a b l e p e r u n i t i n m u l t i p l e d w e l l i n g s t r u c t u r e s . I n 1969 a l l i n t e r e s t r a t e c e i l i n g s were removed. The maximum l o a n amounts f o r a p a r t m e n t b u i l d i n g s were i n c r e a s e d f r o m $12,000 t o $18,000 p e r u n i t i n 1968, and f u r t h e r i n c r e a s e d i n 1972 t o $23,000. ( c ) Tax L e g i s l a t i o n I n November 1971, new t a x l e g i s l a t i o n was p a s s e d w h i c h r e d u c e d t h e b e n e f i t s o f r e a l e s t a t e i n v e s t m e n t s . Income l o s s e s f r o m r e a l e s t a t e i n v e s t m e n t s c o u l d o n l y be a p p l i e d t o o t h e r r e a l e s t a t e i n c o m e , r e m o v i n g t h e t a x s h e l t e r b e n e f i t s o f r e a l e s t a t e . A s s e t s o v e r $50,000 r e q u i r e d s e p a r a t e CCA s c h e d u l e s , e l i m i n a t i n g t h e p o s s i b i l i t y o f d e l a y i n g r e c a p t u r e t a x e s t h r o u g h a s s e t p o o l i n g . C a p i t a l g a i n s t a x e s were i n t r o d u c e d f o r f i n a n c i a l a n d r e a l e s t a t e i n v e s t m e n t s . T h e s e were p a y a b l e on i n c r e a s e s i n t h e p r o p e r t y v a l u e o v e r t h e h o l d i n g p e r i o d a n d t h e r e f o r e p a y a b l e upon r e v e r s i o n . (d) M u l t i p l e U n i t R e s i d e n t i a l B u i l d i n g s (MURB) I n r e s p o n s e t o e x t e n s i v e p u b l i c p r e s s u r e , t h e MURB p r o g r a m was i n t r o d u c e d i n t h e November 1974 F e d e r a l B u d g e t . The u n d e r l y i n g r a t i o n a l e f o r t h e p r o g r a m was t h a t i t w o u l d p r o v i d e g r e a t e r r e t u r n s f o r i n v e s t o r s i n t h e m u l t i f a m i l y m a r k e t . H e n c e , c o n s t r u c t i o n o f m u l t i p l e d w e l l i n g s t r u c t u r e s was e x p e c t e d t o i n c r e a s e , p e r m i t t i n g v a c a n c y r a t e s t o r e t u r n t o a " n o r m a l " 31 l e v e l . " E x c e s s r e t u r n s " were a c h e i v e d by p e r m i t t i n g f u l l CCA b e n e f i t s t o be c l a i m e d on MURB's a n d any income l o s s e s c o u l d be used, t o s h e l t e r o t h e r i n c o m e . The MURB p r o g r a m was t o be i n e f f e c t f o r one y e a r , b u t , was e x t e n d e d a n n u a l l y u n t i l 1979. I n O c t o b e r 1980 MURB b e n e f i t s were r e i n s t a t e d u n t i l December 1981. (e) A s s i s t e d R e n t a l P r o g r a m (ARP) The ARP p r o g r a m , i n e f f e c t f r o m 1975 t o 1978, p r o v i d e d r e n t a l u n i t s f o r l o w e r income h o u s e h o l d s . I n i t a l l y , ARP o f f e r e d an a n n u a l g r a n t t o d e v e l o p e r s o f up t o $900 p e r u n i t . T h i s s u b s i d y was p a i d m o n t h l y , a n d r e d u c e d by 10 p e r c e n t e a c h y e a r . I n 1976, t h e g r a n t was c h a n g e d t o a g r a d u a t e d payment l o a n o f up t o $1200 p e r u n i t a n n u a l l y , r e d u c e d by" 10 p e r c e n t p e r y e a r , f o r 10 y e a r s . The l o a n was i n t e r e s t f r e e f o r 10 y e a r s a n d r e g i s t e r e d a s a s e c o n d m o r t g a g e on t h e p r o p e r t y . I n B r i t i s h C o l u m b i a , a c o m p l e m e n t a r y p r o g r a m was i n e f f e c t f r o m 1975 t o 1977, where a g r a n t was a v a i l a b l e f r o m t h e p r o v i n c i a l g o v e r n m e n t of up t o $600 a n n u a l l y p e r u n i t . T h i s was a l s o r e d u c e d by 10 p e r c e n t p e r annum f o r t h e 10 y e a r d u r a t i o n o f t h e a g r e e m e n t . ( f ) R e n t C o n t r o l s R e n t c o n t r o l s were i n i t i a l l y i n t r o d u c e d i n B r i t i s h C o l u m b i a i n 1974 a n d removed w i t h t h e B u d g e t i n J u l y 1983. The e x a c t r e s t r i c t i o n s a n d r e v i e w p r o c e s s u n d e r w e n t s e v e r a l c h a n g e s i n c l u d i n g r e m o v a l o f r e s t r i c t i o n s f o r new u n i t s a n d upward a d j u s t m e n t o f t h e u p p e r l i m i t o f u n i t s t o be e x e m p t e d f r o m c o n t r o l s . The i m p a c t o f r e n t c o n t r o l s on t h e r e n t a l m a r k e t i s 32 c o n t r o v e r s i a l a n d c a n n o t be a d e q u a t e l y " d i s c u s s e d h e r e . 8 The a d d e d u n c e r t a i n t y and g r e a t e r r e s t r i c t i o n s i m p o s e d on t h e m a r k e t a r e c i t e d a s r e d u c i n g t h e a t t r a c t i v e n e s s of i n v e s t m e n t i n t h e r e n t a l m a r k e t . (g) Canada R e n t a l S u p p l y P r o g r a m (CRSP) F o l l o w i n g t h e announcement o f t h e r e m o v a l o f t h e MURB p r o g r a m i n November 1981, CRSP was i n t r o d u c e d . I t s o b j e c t i v e was t o a s s i s t i n t h e c o n s t r u c t i o n o f 15,000 r e n t a l u n i t s a c r o s s C anada i n a r e a s o f t i g h t r e n t a l m a r k e t , t h e r e b y p r e v e n t i n g f u r t h e r d e t e r i o r a t i o n o f v a c a n c y l e v e l s . I n M a r c h 1982 t h e number o f u n i t s was i n c r e a s e d t o 3 0 , 0 0 0 . F i f t e e n y e a r , i n t e r e s t f r e e l o a n s o f up t o $7500 p e r u n i t were made a v a i l a b l e t o a s s i s t i n t h e f i n a n c i n g o f c o n s t r u c t i o n . The l o a n was r e g i s t e r e d a s a s e c o n d m o r t g a g e on t h e p r o p e r t y and w i l l become due and p a y a b l e a t t h e e n d o f t h e 15 y e a r t e r m , o r i f t h e p r o p e r t y i s u s e d f o r o t h e r t h a t r e n t a l r e s i d e n t i a l u n i t s , o r upon d e f a u l t o f t h e f i r s t m o r t g a g e . Comments i n t h e m e d i a a t t h e t i m e o f t h e p r o g r a m s i n c e p t i o n s u g g e s t t h a t t h e amount w o u l d be i n s u f f i c i e n t t o e n c o u r a g e e x t e n s i v e i n v e s t m e n t . 3.4 IMPACTS ON THE MULTI FAMILY MARKET, The a b o v e o u t l i n e o f t h e p r e v a l e n t h o u s i n g p r o g r a m s s u p p o r t s t h e s t a t e m e n t t h a t t h e b i a s o f C a n a d i a n p o s t - w a r h o u s i n g p o l i c y h a s e n c o u r a g e d h o m e o w n e r s h i p . O t h e r d e v e l o p m e n t s s u c h a s amendments t o t h e Bank. A c t , t h e n o n - t a x a t i o n o f c o n s t r u c t i o n m a t e r i a l s a n d z o n i n g 9 w i l l a l s o i n f l u e n c e t h e 33 housing market and c o n s t r u c t i o n a c t i v i t y . In the context of t h i s study, the important i s s u e i s , how w i l l the p o l i c y b i a s toward homeownership and other government programs i n f l u e n c e the demand and supply of m u l t i f a m i l y housing u n i t s ? Any d i s c u s s i o n on t h i s q u e s t i o n may be d i s t o r t e d by l i f e s t y l e p r e f e r e n c e s , other economic c o n d i t i o n s and demographic changes. Assuming that there are only two housing submarkets, r e n t a l and owner-occupied and that these markets are c o m p e t i t i v e , i t co u l d be argued that p o l i c y encouraging homeownerhip w i l l reduce the demand f o r and supply of m u l t i p l e u n i t s . Developing t h i s b r i e f l y , i f the demand f o r homeownership i n c r e a s e s due to a government p o l i c y , the demand f o r r e n t a l accomodation w i l l s i m u l t a neously d e c l i n e , assuming no change i n household formation as a r e s u l t of that p o l i c y . Since the short run supply curve f o r housing i s i n e l a s t i c , the p r i c e of r e n t a l u n i t s w i l l d e c l i n e , followed by a d e c l i n e i n the q u a n t i t y c o n s t r u c t e d . S i m i l a r l y , the r i s e i n the demand f o r s i n g l e u n i t s w i l l r e s u l t in a p r i c e i n c r e a s e and subsequent i n c r e a s e i n the q u a n t i t y of u n i t s c o n s t r u c t e d . T h i s l i n e of argument ignores changes i n demand from the demographic s t r u c t u r e and l i f e s t y l e p r e f e r e n c e s , and the p o s s i b i l i t y of e l a s t i c i t y i n the supply curve provided by i n v e n t o r i e s and u n i t s under c o n s t r u c t i o n . (These c o u l d be added to the stock i n the short run.) I t a l s o assumes that government p o l i c i e s which reduce the cost of s i n g l e f a m i l y housing do not cause an i n c r e a s e i n household formation. The h i g h e s t r e n t a l component of the p o p u l a t i o n i s the 15-29 34 age c o h o r t . As t h e "baby boom" segment moved t h r o u g h t h e s e y e a r s t h e demand f o r r e n t a l u n i t s i n c r e a s e d . H owever, w i t h t h e a g i n g o f t h i s segment o f t h e p o p u l a t i o n a nd t h e d e c l i n e i n t h e number o f p e o p l e i n t h e y o u n g e r a n d h i g h r e n t a l age c o h o r t s , g r e a t e r demand i s e x p e c t e d f o r o w n e r s h i p u n i t s a n d l e s s e m p h a s i s on r e n t a l u n i t s . A f u r t h e r c o n s i d e r a t i o n i s t h e common a t t i t u d e o f h o u s i n g p r o v i d i n g a. "hedge" a g a i n s t i n f l a t i o n , t h e r e b y o f f e r i n g i n v e s t m e n t a n d s h e l t e r c o m p o n e n t s . 1 0 S i n c e t h e p r i c e o f h o u s i n g i s commonly p e r c e i v e d t o have k e p t p a c e o r s u r p a s s e d i n f l a t i o n , a n d t h e r e a r e no t a x e s on t h e i m p u t e d r e n t s o r c a p i t a l g a i n s f r o m h o u s i n g , h o u s e h o l d s w h i c h may n o t have e n t e r e d t h e o w n e r s h i p m a r k e t p r e v i o u s l y a r e d o i n g so f o r t h e i n v e s t m e n t o p p o r t u n i t i e s . D e m o g r a p h i c c h a n g e s , l i f e s t y l e p r e f e r e n c e s a n d t h e i n v e s t m e n t b e n e f i t s o f h o u s i n g have i n c r e a s e d t h e demand f o r o w n e r s h i p . The d e c l i n e i n m u l t i f a m i l y c o n s t r u c t i o n o v e r t h e p a s t two d e c a d e s i s t h e r e f o r e n o t an u n r e a s o n a b l e e x p e c t a t i o n . B u t , t h e q u e s t i o n o f how g o v e r n m e n t p o l i c y a f f e c t t h e m u l t i f a m i l y h o u s i n g m a r k e t r e m a i n s . The t a x c h a n g e s i n 1971 a n d t h e i n t r o d u c t i o n o f r e n t c o n t r o l s i n 1974 a r e q u o t e d a s two s i g n i f i c a n t f o r c e s d e t e r i n g i n v e s t m e n t i n t h e m u l t i f a m i l y h o u s i n g m a r k e t . The MURB p r o g r a m was d e s i g n e d t o e n c o u r a g e p r i v a t e i n v e s t m e n t i n t h e m u l t i f a m i l y h o u s i n g m a r k e t . Two c o n f l i c t i n g v i e w s on t h e s u c c e s s o f t h e p r o g r a m h a v e been o f f e r e d . The f i r s t s u g g e s t s t h a t t h e l e v e l o f s t a r t s was s i g n i f i c a n t l y i n c r e a s e d f o r t h e d u r a t i o n o f t h e p r o g r a m . 1 1 The a l t e r n a t e a r g u m e n t i s t h a t t h e b e n e f i t s o f t h e 35 p r o g r a m were s h o r t l i v e d , w i t h t h e b e n e f i t s b e i n g c a p i t a l i z e d i n t o l a n d p r i c e s . 1 2 An e x a m i n a t i o n o f t h e d a t a s u g g e s t s t h a t m u l t i f a m i l y s t a r t s were g e n e r a l l y d e c l i n i n g i n t h e 1 9 7 0 ' s , w i t h an i n c r e a s e i n 1975 when t h e p r o g r a m was i n t r o d u c e d a n d a s u d d e n s u r g e i n 1981 w i t h t h e announcement o f t h e p r o g r a m ' s c a n c e l l a t i o n . S i m u l t a n e o u s p r o g r a m s , s u c h a s ARP, AHOP and g o v e r n m e n t g r a n t s c l o u d a ny i n t e r p r e t a t i o n o f t h e s p e c i f i c i m p a c t s o f t h e MURB p r o g r a m . A n o t h e r p o s s i b l e i m p a c t o f t h e MURB p r o g r a m , s u g g e s t e d by S m i t h ( l 9 8 l ) , i s a s h i f t i n t h e s e a s o n a l i t y o f m u l t i f a m i l y c o n s t r u c t i o n . I n a n t i c i p a t i o n o f r e m o v a l o f MURB b e n e f i t s e a c h y e a r i n t h e F e d e r a l B u d g e t , S m i t h p r o p o s e s t h e r e i s a t e n d e n c y f o r b u i l d e r s t o i n c r e a s e s t a r t s i n t h e f o u r t h q u a r t e r . G o v ernment i n t e r v e n t i o n i n t h e h o u s i n g m a r k e t h a s u n d o u b t e d l y c h a n g e d t h e m a r k e t s t r u c t u r e a n d t h e r e s p o n s i v e n e s s o f b u i l d e r s t o demand a nd o t h e r . e c o n o m i c v a r i a b l e s . A l t h o u g h i t c a n be a r g u e d t h a t t h e h o u s i n g m a r k e t i s e f f i c i e n t , c u r r e n t m a r k e t p a r t i c i p a n t s r e c o g n i z e t h e s t r o n g i n f l u e n c e o f g o v e r n m e n t p r o g r a m s o v e r new c o n s t r u c t i o n . W i t h o u t t h e b e n e f i t s o f some g o v e r n m e n t i n c e n t i v e scheme, c o n s t r u c t i o n i s d r a s t i c a l l y s c a l e d down. A l t e r n a t i v e l y , c o n s t r u c t i o n p l a n s a r e e s c a l a t e d upon t h e announcement o f new i n c e n t i v e p r o g r a m s . The r a t i o n a l e f o r g o v e r n m e n t p r o g r a m s h a s f o c u s e d on p r o v i d i n g " a f f o r d a b l e a n d a d e q u a t e " h o u s i n g a n d t o r e d u c e t h e c y c l i c a l n a t u r e o f r e s i d e n t i a l c o n s t r u c t i o n . I t may be p o s s i b l e t o a r g u e t h a t t h e r e s i d e n t i a l c o n s t r u c t i o n i n d u s t r y i s now s o d e p e n d e n t upon i n c e n t i v e p r o g r a m s t h a t t h e s e a r e a d r i v i n g f o r c e i n t h e h o u s i n g 36 m a r k e t . I f t h i s i s t h e r e a l m a r k e t s c e n a r i o , t h e t a s k o f d e t e r m i n i n g t h e m a r k e t d y n a m i c s becomes i n c r e a s i n g l y d i f f i c u l t s i n c e t h e p r e c i s e i m p a c t s o f g o v e r n m e n t p r o g r a m s a r e n o t known w i t h any a c c u r a c y . T h e r e i s a l s o a n e e d t o d i s t i n g u i s h m a r k e t an d n o n - m a r k e t h o u s i n g c o n s t r u c t i o n t o e n a b l e a b e t t e r u n d e r s t a n d i n g o f p o l i c y i m p a c t s a n d t h e d e t e r m i n a t i o n of e c o n o m i c v a r i a b l e s i n f l u e n c i n g t h e m a r k e t . A l t h o u g h dummy v a r i a b l e s c a n be u s e d i n t h e e m p i r i c a l a n a l y s i s d u r i n g t h e p e r i o d s where p r o g r a m s were i m p l e m e n t e d , t h e r e i s l i t t l e e v i d e n c e t o s u p p o r t t h e d e s i g n and s t r u c t u r e o f t h e s e v a r i a b l e s . 37 4. THEORETICAL MODEL P r e v i o u s r e s e a r c h h a s e s t i m a t e d t h e l e v e l o f s t a r t s u s i n g r e d u c e d f o r m e q u a t i o n s b a s e d on e c o n o m i c v a r i a b l e s o r p r o x i e s , w i t h l i t t l e d i s c u s s i o n d e v o t e d t o t h e i n v e n t o r y . o f c o m p l e t e d u n i t s o r u n i t s u n d e r c o n s t r u c t i o n m a i n t a i n e d by b u i l d e r s . The m o d e l c o m p o n e n t s and l a g s t r u c t u r e a d o p t e d d e p e n d upon t h e e x a c t s p e c i f i c a t i o n , n a t u r e a n d p u r p o s e p f t h e m o d e l . An a l t e r n a t e a p p r o a c h was t a k e n by M a i s e l ( 1 9 6 3 ) , who a t t e m p t e d t o d e v e l o p an i n v e n t o r y a d j u s t m e n t m o d e l where t h e c o n s t r u c t i o n l e v e l o f new h o u s i n g u n i t s was s e t t o s a t i s f y e x p e c t e d demand a n d m a i n t a i n a d e s i r e d l e v e l o f i n v e n t o r y . R o s en ( 1 9 7 9 ) e n d o r s e d t h e c o n c e p t o f an i n v e n t o r y a p p r o a c h a n d i n d i c a t e d t h a t t h e i n i t i a l r e a c t i o n t o an i n c r e a s e d demand w o u l d be r e d u c e d i n v e n t o r i e s . B u i l d e r s w o u l d i n c r e a s e c o n s t r u c t i o n i n r e s p o n s e t o r e d u c e d i n v e n t o r i e s , d e p e n d i n g upon o t h e r e c o n o m i c c o n d i t i o n s . a n d t h e c u r r e n t d e s i r e d l e v e l o f i n v e n t o r y . A s s u m i n g t h e h o u s i n g m a r k e t i s i n e q u i l i b r i u m , some e x o g e n e o u s f o r c e c o u l d i n i t i a t e an i n c r e a s e i n t h e demand f o r h o u s i n g u n i t s w h i c h w o u l d be met t h r o u g h e x i s t i n g v a c a n c i e s a n d i n v e n t o r i e s o f c o m p l e t e d a n d u n o c c u p i e d u n i t s . I f b u i l d e r s d e s i r e t o m a i n t a i n a c o n s t a n t l e v e l o f i n v e n t o r y , t h e l e v e l o f s t a r t s i n t h e f o l l o w i n g p e r i o d s w o u l d be i n c r e a s e d t o r e p l e n i s h i n v e n t o r i e s a n d meet e x p e c t e d c o n t i n u e d i n c r e a s e s i n demand. The r e v e r s e p r o c e s s n a t u r a l l y f o l l o w s ; s t a r t s w o u l d be r e d u c e d i f demand d e c l i n e d a n d i n v e n t o r i e s i n c r e a s e d . I t i s a l s o p o s s i b l e f o r t h e d e s i r e d l e v e l o f i n v e n t o r y t o c h a n g e b a s e d on 38 b u i l d e r s o r i n v e s t o r s c o s t s t o m a i n t a i n v a c a n t u n i t s , a n d e x p e c t a t i o n s o f f u t u r e demand. G i v e n t h i s e x p e c t e d a d j u s t m e n t p r o c e s s i n t h e h o u s i n g m a r k e t , i t i s s u g g e s t e d t h a t an i n v e n t o r y a d j u s t m e n t m o del w o u l d be a p p r o p r i a t e t o e s t i m a t e t h e l e v e l o f s t a r t s i n a g i v e n p e r i o d . I t may be p o s s i b l e t o e x p a n d t h e f o l l o w i n g t h e o r e t i c a l m o d e l t o t h e s i n g l e f a m i l y h o u s i n g m a r k e t , b u t f o r t h e p u r p o s e o f t h i s p a p e r , o n l y t h e m u l t i f a m i l y m a r k e t w i l l be r e v i e w e d . 4.1 INVENTORY ADJUSTMENT CONCEPT The t h e o r e t i c a l i n v e n t o r y a d j u s t m e n t m o d e l u s e s e x p e c t e d a n d a c t u a l s a l e s a n d d e v i a t i o n s f r o m p r o j e c t e d s a l e s t o e s t i m a t e t h e p r o d u c t i o n f o r . a g i v e n p e r i o d . I f s a l e s e x c e e d e x p e c t a t i o n s , p r o d u c e r s may r e p s o n d t h r o u g h : p r i c e a d j u s t m e n t s , i n c r e a s e s i n p r o d u c t i o n s c h e d u l e s , p e r m i t t i n g , some u n s a t i s f i e d demand, o r i n v e n t o r y r e d u c t i o n s . P r i c e a d j u s t m e n t s a r e g e n e r a l l y r e s i s t e d s i n c e t h e m a r k e t may i n t e r p r e t t h i s a s some e r r o r on t h e p a r t o f t h e p r o d u c e r , r e d u c i n g c o n s u m e r c o n f i d e n c e . S i n c e i m m e d i a t e p r o d u c t i o n c h a n g e s a r e g e n e r a l l y c o s t l y t h e y a r e a v o i d e d a nd p r o d u c e r s p r e f e r t o c h a n g e p r o d u c t i o n l e v e l s g r a d u a l l y i n r e s p o n s e t o m a r k e t demand. B a c k l o g o r d e r s p r o v i d e an i n d i c a t o r o f p e n t - u p demand, b u t u n s a t i s f i e d demand i s g e n e r a l l y d i f f i c u l t t o d e t e r m i n e . G i v e n t h e s e a l t e r n a t i v e s , a n d t h e a s s u m p t i o n t h a t i t i s p o s s i b l e t o m a i n t a i n i n v e n t o r i e s o f c o m p l e t e d g o o d s , t h e l o g i c a l c o n c l u s i o n i s t h a t i n v e n t o r i e s w i l l be u s e d t o b u f f e r d i s c r e p a n c i e s b e t w e e n e x p e c t e d a n d a c t u a l s a l e s . When a c t u a l s a l e s e x c e e d e x p e c t e d s a l e s , i n v e n t o r i e s 39 w i l l be. reduced. Conversely, i f a c t u a l s a l e s are l e s s than p r o j e c t e d , the excess p r o d u c t i o n w i l l be maintained as in v e n t o r y . Presumably, there i s some d e s i r e d l e v e l of inventory which producers wish to maintain and any change i n the l e v e l of inventor y due to e x c e s s ( d e f i c i t ) s a l e s w i l l then be r e f l e c t e d in pro d u c t i o n l e v e l s . However, p r o d u c t i o n changes w i l l not be through d r a s t i c r e d u c t i o n s ( i n c r e a s e s ) , r a t h e r , there w i l l be some r a t e of adjustment between changes i n i n v e n t o r i e s and prod u c t i o n l e v e l s , r e f e r r e d to as the a c c e l e r a t o r . A l s o , the d e s i r e d l e v e l of i n v e n t o r i e s may not be co n s t a n t , but w i l l a d j u s t to c u r r e n t and expected economic c o n d i t i o n s , or other exogeneous f o r c e s . The model t h e r e f o r e i n c o r p o r a t e s a c o e f f i c i e n t of adjustment to represent the f l u c t u a t i o n s i n the d e s i r e d i n v e n t o r y l e v e l . F i n a l l y , assuming producers are not myopic and have some e x p e c t a t i o n s of f u t u r e s a l e s , a c o e f f i c i e n t can be i n c o r p o r a t e d to r e f l e c t the magnitude and d i r e c t i o n of expected changes i n s a l e s . Any e s t i m a t i o n f o r production w i l l then i n c l u d e : p r o d u c t i o n f o r expected s a l e s , production to r e p l e n i s h inventory and p r o d u c t i o n to ad j u s t output to a given p r o p o r t i o n of expected s a l e s , assuming that i t i s not p o s s i b l e to a d j u s t immediately to a new l e v e l of expected s a l e s . The above d i s c u s s i o n b r i e f l y d e s c r i b e s the process of inventor y adjustments, how producers may respond to changes i n demand and the impact on i n v e n t o r y and p r o d u c t i o n l e v e l s . 1 3 F i g u r e 4.1 presents the expected p a t t e r n s of i n v e n t o r i e s , s a l e s and p r o d u c t i o n . Assuming i n i t i a l e q u i l i b r i u m , p r o d u c t i o n w i l l 40 Figure 4.1 INVENTORY ADJUSTMENT PROCESS 1. Increase in demand. 2. Decrease in inventory. 3. Increase in construction to meet demand and reple n i s h inventory. 4. Adjustment of construction and inventory to new eq u i l i b r i u m . 41 be f o r s a l e s a n d i n v e n t o r i e s w i l l be m a i n t a i n e d a t some d e s i r e d l e v e l . I f some i n i t i a l new, u n a n t i c i p a t e d demand i s g e n e r a t e d by an e x o g e n e o u s f o r c e , t h e n s a l e s w i l l i n c r e a s e and i n v e n t o r i e s s u b s e q u e n t l y r e d u c e d . P r o d u c t i o n w i l l t h e n be i n c r e a s e d t o r e t u r n i n v e n t o r i e s t o t h e d e s i r e d l e v e l , h o w e v e r , o v e r c o m p e n s a t i o n i s l i k e l y . P r o d u c t i o n a n d i n v e n t o r y l e v e l s c o n t i n u e t o a d j u s t , o s c i l l a t i n g a b o u t t h e new e q u i l i b r i u m . The d i r e c t a p p l i c a t i o n o f t h i s t h e o r e t i c a l m o d e l t o t h e r e n t a l h o u s i n g m a r k e t h a s s e v e r a l i n h e r e n t d i f f i c u l t i e s . F i r s t , t h e a b s o r p t i o n o f new u n i t s may be u s e d a s a measure o f s a l e s , b u t t h e r e i s a l s o a l a r g e " u s e d g o o d s m a r k e t " i n t h e e x i s t i n g s t o c k . S e c o n d , e x c e s s demand may be i n d i c a t e d t h r o u g h v a c a n c y r a t e s , b u t may be met t h r o u g h a l t e r n a t e h o u s i n g s u c h a s c o n v e r s i o n s . T h i r d , i n t h e t h e o r e t i c a l s p e c i f i c a t i o n o f t h e i n v e n t o r y a d j u s t m e n t m o d e l , p r o d u c t i o n i s e s t i m a t e d u s i n g p r o d u c t i o n f r o m p r e v i o u s p e r i o d s , b u t d o e s n o t m e a s u r e t h e p r e c i s e i m p a c t o f i n v e n t o r y l e v e l s on p r o d u c t i o n . F i n a l l y , t h e r e i s no d i s t i n c t i o n f o r i n v e n t o r y u n d e r c o n s t r u c t i o n (work i n p r o g r e s s ) a nd c o m p l e t e d , u n o c c u p i e d u n i t s ( f i n i s h e d i n v e n t o r y ) . H i r s c h a n d L o v e l l ( 1 9 6 9 ) p o o l t h e s e two c o m p o n e n t s i n an e x a m i n a t i o n o f d u r a b l e a n d n o n - d u r a b l e m a n u f a c t u r i n g , h o w e v e r , a d i s t i n c t i o n may be i m p o r t a n t . i n t h e m u l t i f a m i l y m a r k e t t o i n c l u d e t h e i m p a c t o f a l o n g c o n s t r u c t i o n h o r i z o n . R e s t r u c t u r i n g t h e i n v e n t o r y a d j u s t m e n t p r o c e s s t o i n c l u d e a d i s t i n c t i o n b e t w e e n i n v e n t o r y a n d u n i t s u n d e r c o n s t r u c t i o n may s u g g e s t a two s t a g e r e s p o n s e m o d e l . The i n i t i a l r e s p o n s e t o an i n c r e a s e d demand w o u l d be an i n c r e a s e i n c o m p l e t i o n s a s t h e s e 42 w o u l d h a v e a more i m m e d i a t e i m p a c t on t h e i n v e n t o r y l e v e l . U n i t s u n d e r c o n s t r u c t i o n w o u l d t h e n be r e d u c e d , and a s s u m i n g t h a t t h e r e i s some d e s i r e d l e v e l o f u n i t s u n d e r c o n s t r u c t i o n t o be m a i n t a i n e d , s t a r t s w o u l d then, be i n c r e a s e d . T h i s s u g g e s t s t h a t s t a r t s w i l l h a v e a g r e a t e r l a g b e h i n d i n v e n t o r y c h a n g e s , a s s u m i n g t h a t when c o m p l e t i o n s i n c r e a s e t h e r e i s no s i m u l t a n e o u s i n c r e a s e i n s t a r t s . A more p r o b a b l e s o l u t i o n i s t h a t s t a r t s w i l l r e s p o n d t o c h a n g e s i n i n v e n t o r y a n d u n i t s u n d e r c o n s t r u c t i o n . 4.2 MODEL S P E C I F I C A T I O N B e f o r e p r e s e n t i n g t h e o v e r a l l t h e o r e t i c a l m o d e l , two i s s u e s s h o u l d be c o n s i d e r e d . F i r s t , what i s d e f i n e d a s a . h o u s i n g u n i t ? S e c o n d , d o e s m u l t i f a m i l y h o u s i n g i n c l u d e p u b l i c a n d p r i v a t e u n i t s , r e n t a l a n d o w n e r s h i p u n i t s ? R a t h e r t h a n u s i n g t h e number of h o u s i n g u n i t s , some p r e v i o u s s t u d i e s h a v e a t t e m p t e d t o s t a n d a r d i z e a m e a s u r e o f h o u s i n g s e r v i c e s , w h i l e o t h e r s h ave c o n s i d e r e d e x p e n d i t u r e s a s a more a p p r o p r i a t e m e a sure o f c o n s t r u c t i o n a c t i v i t y ( J a f f e e & R o s e n , 1 9 7 9 ) . M e a s u r e s o f h o u s i n g s e r v i c e s o r e x p e n d i t u r e s p r o v i d e an i n d i c a t o r o f a c t i v i t y i n t h e m a r k e t , h o w e v e r , i t i s d i f f i c u l t t o c o n v e r t t h e s e t o t h e a c t u a l number o f u n i t s s t a r t e d , c o m p l e t e d , a b s o r b e d , o r t h e number o f u n i t s i n i n v e n t o r y o r e x i s t i n g s t o c k . I t i s t h e number o f i n d i v i d u a l h o u s i n g u n i t s w h i c h i s i m p o r t a n t i n r e l a t i n g t h e s u p p l y a n d demand f o r h o u s i n g , a n d w h i c h i s most a p p l i c a b l e f o r p o l i c y a n d p l a n n i n g d e c i s i o n s . C o n s e q u e n t l y , d e s p i t e p o s s i b l e d i s c r e p a n c i e s w i t h r e s p e c t t o h o u s i n g q u a l i t y , 43 age and s i z e , h o u s i n g w i l l be m e a s u r e d a s t h e raw number o f u n i t s . The s e c o n d i s s u e , w h i c h a d d r e s s e s t h e d e f i n i t i o n o f m u l t i f a m i l y u n i t s , c a n be e a s i l y r e s o l v e d i n t h e t h e o r e t i c a l c o n t e x t , b u t c r e a t e s some d i f f i c u l t y f o r t h e e m p i r i c a l a n a l y s i s . T r a d i t i o n a l l y , t h e s t r u c t u r e t y p e ( s i n g l e f a m i l y o r m u l t i f a m i l y ) a n d t e n u r e ( o w n e r s h i p o r r e n t a l ) h a v e been assumed t o be s y n onymous. To own i m p l i e d a s i n g l e f a m i l y o r d e t a c h e d u n i t a n d t o r e n t i m p l i e d a m u l t i f a m i l y u n i t . W i t h t h e i n t r o d u c t i o n o f s t r a t a t i t l e s e n a b l i n g o w n e r s h i p o f m u l t i f a m i l y u n i t s , t h e r e n t a l o f d e t a c h e d u n i t s , t h e c o n v e r s i o n o f d e t a c h e d h o u s i n g t o d u p l e x e s and t h e g r e a t e r a c c e p t a n c e o f row h o u s i n g , t h i s g e n e r a l i z a t i o n may be an i n a c c u r a t e r e p r e s e n t a t i o n o f t h e m a r k e t . T h e s e c h a n g e s i n t h e f o r m o f t h e h o u s i n g s t o c k have i n c r e a s e d t h e s u b s t i t u t a b i l i t y b e t w e e n s t r u c t u r e t y p e s , i n c r e a s i n g t h e d i f f i c u l t y i n e x a m i n i n g s p e c i f i c s u b m a r k e t s w i t h i n t h e t o t a l h o u s i n g m a r k e t . F o r t h e d e v e l o p m e n t o f t h e t h e o r e t i c a l m o d e l , i t i s a ssumed t h a t t h e s u b m a r k e t b e i n g e x a m i n e d i s t h e p r i v a t e l y i n i t i a t e d , r e n t a l , m u l t i f a m i l y ( a p a r t m e n t ) h o u s i n g m a r k e t . The d i f f i c u l t i e s w i t h t h i s d e f i n i t i o n f o r t h e e m p i r i c a l a n a l y s i s w i l l be a d d r e s s e d i n t h e s e c t i o n s on t h e d a t a a n d t h e e m p i r i c a l r e s u l t s . 4.2.1 O v e r a l l M o d e l The t h r e e key c o m p o n e n t s o f t h e o v e r a l l m o d e l c o r r e s p o n d t o t h e c o m p o n e n t s o f m a n u f a c t u r i n g i n v e n t o r y m o d e l s w i t h t h e m a j o r d i f f e r e n c e s b e i n g t h e d u r a b i l i t y a n d i m m o b i l i t y o f h o u s i n g u n i t s 44 and l o n g e r c o n s t r u c t i o n t i m e . T h e s e c o m p o n e n t s i n c l u d e t h e r a t e a t w h i c h new u n i t s a r e a b s o r b e d by t h e m a r k e t ( s a l e s / r e n t a l ) , t h e number o f u n i t s a v a i l a b l e ( i n v e n t o r y ) a n d t h e l e v e l o f s t a r t s ( p r o d u c t i o n ) . The s t r u c t u r e o f t h e m o d e l i s s u c h t h a t c h a n g e s i n e a c h component may be i n i t i a t e d f r o m two s o u r c e s w i t h t h e e x i s t i n g s t o c k a s t h e f o c u s o f m a r k e t a d j u s t m e n t s . ( s e e F i g u r e 4.2) A b s o r p t i o n s ( s a l e s ) w i l l d e p e n d upon t h e number o f new h o u s e h o l d s d e m a n d i n g r e n t a l a c c o m o d a t i o n . T h i s w i l l a d j u s t a c c o r d i n g t o t h e d e m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n a n d o t h e r e c o n o m i c c o n d i t i o n s . 1 * The number o f u n i t s i n . i n v e n t o r y a v a i l a b l e f o r r e n t ( o r s a l e ) w i l l i n c r e a s e ( d e c r e a s e ) i f t h e r a t e o f a b s o r p t i o n i n c r e a s e s ( d e c r e a s e s ) , a s s u m i n g no new u n i t s a r e s i m u l t a n e o u s l y c o n s t r u c t e d t o meet t h e c h a n g e i n demand. I n v e n t o r i e s l e v e l s w i l l a l s o r e f l e c t b u i l d e r s ' o r i n v e s t o r s ' d e s i r e d l e v e l o f i n v e n t o r y . P r e s u m a b l y , i f e c o n o m i c c o n d i t i o n s a r e u n f a v o u r a b l e f o r h o l d i n g v a c a n t u n i t s , s t a r t s w i l l be r e d u c e d a n d t h e l e v e l o f i n v e n t o r y w i l l be p e r m i t t e d t o d e c l i n e . C o n v e r s e l y , a s t h e d e s i r e d l e v e l o f i n v e n t o r y i n c r e a s e s , s t a r t s w i l l be g e n e r a t e d t o r e p l e n i s h i n v e n t o r i e s . The p r o d u c t i o n o f new u n i t s w i l l be t o meet t h e e x p e c t e d r a t e o f a b s o r p t i o n , a n d t o a d j u s t i n v e n t o r i e s a c c o r d i n g l y . T h i s . i s i n k e e p i n g w i t h t h e t h e o r e t i c a l m o d e l where p r o d u c t i o n i s f o r a n t i c i p a t e d s a l e s a n d i n v e n t o r y r e p l a c e m e n t ( d e c l i n e ) . F i n a l l y , a s u n i t s a r e c o m p l e t e d t h e y become p a r t o f t h e e x i s t i n g h o u s i n g s t o c k . The c e n t r a l f o c u s i s t h e e x i s t i n g s t o c k w h i c h i s i n c r e a s e d w i t h c o m p l e t i o n s a n d w i l l i n f l u e n c e t h e a b s o r p t i o n o f new u n i t s . The number o f <+5 Figure 4.2 MODEL STRUCTURE MULTI FAMILY HOUSING STARTS H o u s e h o l d F o r m a t i o n <= V A b s o r p t i o n S t o c k E c o n o m i c F a c t o r s I n v e n t o r y /w Compl e t i o n s ^ > S t a r t s 46 v a c a n t u n i t s i n t h e e x i s t i n g s t o c k , t h e c o n d i t i o n a n d l o c a t i o n of e x i s t i n g u n i t s w i l l i n f l u e n c e t h e d e s i r a b i l i t y o f new a n d e x i s t i n g h o u s i n g u n i t s . T h i s w i l l s u b s e q u e n t l y i n f l u e n c e t h e r a t e o f a b s o r p t i o n o f new u n i t s , i n i t i a t i n g f u r t h e r a d j u s t m e n t s i n t h e s y s t e m t h r o u g h i n v e n t o r y l e v e l s . 4.2.2 Demand The demand f o r h o u s i n g u n i t s i s f r o m t h e f o r m a t i o n o f new h o u s e h o l d s and f r o m e x i s t i n g h o u s e h o l d s c h a n g i n g t h e i r t e n u r e a n d / o r s t r u c t u r e t y p e . The number o f new h o u s e h o l d s c a n be e s t i m a t e d g i v e n t h e d e m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n , t h e n a t u r a l a g i n g p r o c e s s a n d e x p e c t e d r e n t a l p a t t e r n s . However, t h e a c t u a l number o f h o u s e h o l d s a nd t h e t y p e o f u n i t s demanded w i l l be i n f l u e n c e d by e c o n o m i c c o n d i t i o n s a n d l i f e s t y l e p r e f e r e n c e s . The d e c i s i o n f o r a h o u s e h o l d t o consume a d d i t i o n a l ( o r f e w e r ) h o u s i n g u n i t s c a n be s u b d i v i d e d i n t o t h r e e s t e p s . F i r s t , t h e d e c i s i o n t o f o r m a h o u s e h o l d , s e c o n d , t h e t e n u r e t y p e p r e f e r r e d ( o w n e r s h i p o r r e n t a l ) ; t h i r d , t h e s t r u c t u r a l t y p e o f h o u s i n g s o u g h t ( d e t a c h e d , row, a p a r t m e n t , e t c . ) . S t e e l e ( 1 9 79) s u g g e s t e d t h a t t h e t h i r d d e c i s i o n s h o u l d be e x p e n d i t u r e ; t h e amount a h o u s e h o l d c h o o s e t o , o r c o u l d a f f o r d t o s p e n d on h o u s i n g . As s u c h , e x p e n d i t u r e s c o u l d be i n t e r p r e t e d a s an a d d i t i o n a l s t e p . S i n c e t h e d e c i s i o n s o f t e n u r e a n d s t r u c t u r e w o u l d be r e s t r i c t e d by any e x p e n d i t u r e c o n s t r a i n t s , t h e e x p e n d i t u r e r e s t r i c t i o n i s i m p l i c i t l y c o n s i d e r e d a n d does n o t r e q u i r e s p e c i f i c a t i o n . As m e n t i o n e d , c h a n g e i n t h e number o f h o u s e h o l d s may r e s u l t 47 f r o m t h e d e m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n , o r e c o n o m i c c o n d i t i o n s a f f e c t i n g t h e d e c i s i o n t o f o r m a h o u s e h o l d . A s s u m i n g t h e r e was no c h a n g e i n t h e r a t e a t w h i c h e a c h age c o h o r t f o r m e d h o u s e h o l d s , t h e demand f o r h o u s i n g u n i t s c o u l d be e a s i l y e s t i m a t e d f r o m k n o w l e d g e o f t h e e x i s t i n g p o p u l a t i o n s t r u c t u r e . T h i s i g n o r e s t h e p o s s i b i l i t y o f m i g r a t i o n i n t h e r e g i o n , and any e c o n o m i c v a r i a b l e s c o n s i d e r e d i n t h e h o u s e h o l d f o r m a t i o n d e c i s i o n . The e c o n o m i c v e c t o r w i l l i n c l u d e r e a l d i s p o s a b l e i n c o m e s , t h e unemployment r a t e , r e a l r e n t s and t h e r e a l p r i c e o f h o u s i n g . The e q u a t i o n t o e s t i m a t e t h e number o f h o u s e h o l d s t h e n becomes: HH = H ( Y d , U , R / C P I , P h / C P I , H H ( - 1 ) , p o p ) w h e r e : HH number o f h o u s e h o l d s Yd r e a l d i s p o s a b l e income U unemployment r a t e R/CPI r e a l r e n t s Ph/CPI r e a l p r i c e o f h o u s i n g HH(-1) number o f h o u s e h o l d s i n p r e v i o u s p e r i o d pop p o p u l a t i o n ( b y age a n d s e x ) As i n c o m e s r i s e , c e t e r i s p a r i b u s , t h e r e w i l l be a t e n d e n c y t o w a r d more r a p i d h o u s e h o l d f o r m a t i o n w i t h t h e u n d o u b l i n g o f e x i s t i n g h o u s e h o l d s , more one p e r s o n h o u s e h o l d s , e t c . The q u e s t i o n a r i s e s , w h i c h i n c o m e m e a s u r e most a c c u r a t e l y r e f l e c t s h o u s e h o l d b e h a v i o u r ? I s t h e r e l e v a n t income m e a s u r e p e r m a n e n t o r m e a s u r e d i n c o m e , p e r c a p i t a d i s p o s a b l e income o r some o t h e r 48 measure? The general argument suggests that housing purchases depend upon p e r c e p t i o n s of permanent d i s p o s a b l e income per household and t h e r e f o r e t h i s should be the r e l e v a n t measure. In the short term, household formation may be delayed due to cash flow c o n s t r a i n t s , s u p p o r t i n g the use of measured d i s p o s a b l e income. An increase i n unemployment should have a negative impact on household formation. However, unemployment may be r e f l e c t e d i n measured incomes, and only delay household formation d e c i s i o n s . I t i s expected that unemployment may not prove s i g n i f i c a n t i n the long run a n a l y s i s , but i s mentioned f o r completeness i n the t h e o r e t i c a l framework. Permanent d i s p o s a b l e income and unemployment r a t e s combined are suggested to ensure the short run and long run impacts of income are i n c l u d e d . Assuming e q u i l i b r i u m , the user c o s t s of owning a housing u n i t should equal the rent on a s i m i l a r housing u n i t , t a k i n g i n t o account a l l tax b e n e f i t s , and a p p r e c i a t i o n of the housing u n i t . Since i t i s expected that these two f a c t o r s may not be i n e q u i l i b r i u m , both should be i n c l u d e d i n the household formation equation. The a l t e r n a t e argument i s that new households have a gr e a t e r tendency to r e n t , and t h e r e f o r e only r e n t a l c o s t s need be i n c l u d e d . There i s no d e f i n i t i v e s o l u t i o n to these arguments, t h e r e f o r e both are i n c l u d e d with the e x p e c t a t i o n that one w i l l prove dominant i n the e m p i r i c a l a n a l y s i s . T h i s r a i s e s the q u e s t i o n of whether the p r i c e of new housing or the expected user c o s t s of housing should be entered i n t o the equation. I t i s then necessary to d e r i v e the c o r r e c t measure of user c o s t s . The above f u n c t i o n a l equation f o r t o t a l households ignores 49 the tenure and s t r u c t u r e c h o i c e s of households. However, the model i s based on r e n t a l , m u l t i f a m i l y housing u n i t s , t h e r e f o r e , the a p p r o p r i a t e household measure i s the number of r e n t a l or m u l t i f a m i l y u n i t d w e l l e r s . Given the demographic s t r u c t u r e of the p o p u l a t i o n and the percentage choosing to rent, i t i s p o s s i b l e to estimate the change i n the number of r e n t a l households from only demographic s h i f t s . Any d e v i a t i o n s from the expected number of r e n t a l households can then be a t t r i b u t e d to economic c o n d i t i o n s or m i g r a t i o n . T h i s i s s i m i l a r to the approach adopted by J a f f e e and Rosen (1979) f o r e s t i m a t i n g the demand f o r owner-occupied housing. The number of new r e n t a l households may then be expressed using the same economic v a r i a b l e s given f o r household formation. There i s no reason to expect that the impact of these v a r i a b l e s w i l l be d i f f e r e n t f o r r e n t a l households than f o r t o t a l households. T h e r e f o r e , the expected impacts w i l l be as o u t l i n e d above. The r e l e v a n t p o p u l a t i o n measure here w i l l be based on the expected r e n t a l households assuming constant headship r a t e s and r e n t a l demand per age c o h o r t . RHH=R(Yd,U,R/CPI,Ph/CPI,pop) The a b s o r p t i o n of m u l t i f a m i l y housing u n i t s i s s i m i l a r to the concept of s a l e s i n the manufacturing i n v e n t o r y adjustment model. I t i s p o s s i b l e to c o n s i d e r the housing stock as a whole and a b s o r p t i o n s as the r e d u c t i o n i n the number of vacant u n i t s a v a i l a b l e , p l u s any newly completed u n i t s which are occupied ( s o l d ) d u r i n g the p e r i o d . T h i s p r o v i d e s an i n d i c a t o r of t o t a l 50 demand f o r mu l t i f a m i l y housing. D i f f i c u l t y a r i s e s i n se p a r a t i n g the demand and subsequent supply changes f o r new u n i t s or e x i s t i n g stock. Since the model developed here i s to provide an e s t i m a t i o n of m u l t i f a m i l y s t a r t s , a more a p p r o p r i a t e measure i s the a b s o r p t i o n of new r e n t a l u n i t s . T h i s i s then d e f i n e d by the f o l l o w i n g i d e n t i t y , assuming that i n v e n t o r i e s r e f e r to completed and unoccupied u n i t s . ABSORB(new) = COMPL + (INV(-1) - INV) where: ABSORB(new) new u n i t s occupied i n the p e r i o d COMPL the mu l t i f a m i l y housing u n i t s completed INV newly completed and unoccupied m u l t i f a m i l y housing u n i t s The r a t e at which these new m u l t i d w e l l i n g u n i t s w i l l be absorbed i n t o the market w i l l be dependent upon the number of vacant u n i t s i n the e x i s t i n g stock, the d e m o l i t i o n of e x i s t i n g u n i t s and the convers i o n of other housing types to r e n t a l u n i t s . In a d d i t i o n , some measure of the expected new r e n t a l households w i l l be i n c l u d e d as an i n d i c a t o r of new demand. The f u n c t i o n a l equation f o r a b s o r p t i o n s w i l l be: ABSORB(new) = A(RHH,vac,demo,conv) where: RHH expected new r e n t a l households vac the vacancy r a t e f o r m u l t i f a m i l y u n i t s demo the number of u n i t s demolished i n the p e r i o d 51 conv the number of new u n i t s from conve r s i o n s Any i n c r e a s e i n the number of r e n t a l households should i n c r e a s e the a b s o r p t i o n of new m u l t i f a m i l y housing u n i t s . However, t h i s may be counteracted i f there are a l a r g e number of e x i s t i n g u n i t s vacant. The change i n the number of r e n t a l households i s expected to have a p o s i t i v e s i g n , while the vacancy rate should be n e g a t i v e . I f there are a l a r g e number of u n i t s demolished i n a p e r i o d , the a b s o r p t i o n of new u n i t s should i n c r e a s e . As the e x i s t i n g stock i s reduced, new u n i t s are r e q u i r e d to r e p l e n i s h the supply of a v a i l a b l e u n i t s . T h i s does not e x p l i c i t l y account f o r the co n v e r s i o n of e x i s t i n g u n i t s to meet any changes i n demand. When va c a n c i e s are low, s i n g l e f a m i l y u n i t s may be duplexed, i n c r e a s i n g the e f f e c t i v e stock without any new c o n s t r u c t i o n . The a b s o r p t i o n of new u n i t s would then be lower than otherwise expected. From t h i s i t i s evident that the p r i c e of housing and r e n t s may not f u l l y r e f l e c t market c o n d i t i o n s . Conversions o f f e r a s u b s t i t u t e good which i s not accounted f o r i n the c l a s s i c a l supply and demand curves f o r m u l t i f a m i l y housing. 4.2.3 Supply The i n v e n t o r y adjustment approach suggests p r o d u c t i o n l e v e l s are based upon the expected s a l e s and the d e s i r e to maintain some inv e n t o r y l e v e l . Within the m u l t i f a m i l y housing market, the a b s o r p t i o n of new u n i t s r e p r e s e n t s the a c t u a l ' s a l e s ' l e v e l . D i f f i c u l t y a r i s e s i n determining i f both in v e n t o r y and u n i t s under c o n s t r u c t i o n should be i n c o r p o r a t e d i n 52 t h e m o d e l ; i s t h e r e some d e s i r e d l e v e l f o r e a c h s e r i e s w h i c h n e e d s t o be c o n s i d e r e d ? I t i s p r o p o s e d t h a t t h e s e m u s t b e d i s t i n g u i s h e d i n l i g h t o f t h e c o n s t r u c t i o n h o r i z o n f o r m u l t i f a m i l y h o u s i n g u n i t s a n d t h e p o s s i b i l i t y t h a t b u i l d e r s w i l l v i e w t h e d e s i r a b i l i t y a n d c o s t s o f m a i n t a i n i n g c o m p l e t e d a n d i n c o m p l e t e u n i t s d i f f e r e n t l y . T h e l e v e l o f i n v e n t o r y d e s i r e d b y b u i l d e r s o r i n v e s t o r s w i l l b e d e p e n d e n t u p o n t h e i r e x p e c t e d p r o f i t s a n d t h e c o s t s o f m a i n t a i n i n g v a c a n t u n i t s . E x p e c t e d p r o f i t a b i l i t y c a n be d e t e r m i n e d f r o m t h e p o t e n t i a l s e l l i n g p r i c e l e s s a n y c o n s t r u c t i o n c o s t s a n d l a n d a c q u i s t i t i o n c o s t s , p l u s ( l e s s ) a n y b e n e f i t s ( c o s t s ) f r o m t a x e s , C CA r e d u c t i o n s a n d c a p i t a l g a i n s . T h i s i s s i m i l a r t o R o s e n ' s r e g i o n a l m o d e l w h e r e p r o f i t i s e s t i m a t e d a s t h e d i s c o u n t e d a f t e r - t a x c a s h f l o w p l u s r e t u r n s a t r e v e r s i o n , l e s s a n y i n i t i a l e x p e n d i t u r e s ( s e e R o s e n , 1 9 7 9 ) . I n a n e f f i c i e n t m a r k e t , i g n o r i n g t a x , l e v e r a g e , o r g o v e r n m e n t p o l i c y , t h e p r o f i t e s t i m a t i o n b e c o m e s 1 5 : ( 1 - v a c ) R E N T - o p e x p P R O F I T = • • CC - LAND c a p r a t e w h e r e : v a c v a c a n c y r a t e R ENT e x p e c t e d r e n t a l i n c o m e o p e x p e x p e c t e d o p e r a t i n g e x p e n s e s c a p r a t e m a r k e t c a p i t a l i z a t i o n r a t e CC c o n s t r u c t i o n c o s t s LAND l a n d c o s t s 53 Then, assuming that some interest rate on investments of equivalent risk would accurately r e f l e c t the cost of holding vacant units, the desired l e v e l of inventory can be expressed as: INV(d) = I(PROFIT, i) An increase in the expected p r o f i t s w i l l increase the attractiveness of holding inventories of multi family units. If other investments are more a t t r a c t i v e , or costs increase through higher interest rates, the desired l e v e l of inventories w i l l decline. Starts w i l l be some proportion of the previous period starts with adjustments to r e f l e c t expected absorptions and deviations of actual inventory levels from the desired l e v e l s . Expected absorptions w i l l be some proportion of the previous period's absorptions, depending on builders or investors market expectations. Adjustments for inventory w i l l be some proportion of the deviation from the desired leveld assuming that there w i l l be a gradual adjustment process. The estimated equation for s tarts i s then: START = « START ( - 1 ) + ABSORB ( - 1 ) + MINV ( -1 )-INV(d) ) + S (UC(-1 )-UC(d) ) where: START multi family unit starts START(-1) previous period starts A B S 0 R B ( - 1 ) previous period absorptions INV ( -1 ) previous period inventory 54 I N V ( d ) d e s i r e d i n v e n t o r y UC (- 1 ) u n i t s u n d e r c o n s t r u c t i o n UC(d) d e s i r e d u n i t s u n d e r c o n s t r u c t i o n T h i s p r o v i d e s t h e b a s i c t h e o r e t i c a l f r a m e w o r k f o r t h e m o d e l e x p l o r e d i n t h i s p a p e r . W i t h i n t h e c o n t e x t o f t h e i n v e n t o r y a d j u s t m e n t m o d e l , e x p e c t e d r e n t a l h o u s e h o l d s w i l l i n f l u e n c e t h e r a t e o f a b s o r p t i o n s f o r new r e n t a l u n i t s . T h e s e c a n be c o n s i d e r e d ' s a l e s ' w i t h i n t h e p r o d u c t i o n f r a m e w o r k . S t a r t s , o r p r o d u c t i o n l e v e l s , w i l l t h e n be s e t t o s a t i s f y any e x p e c t e d demand ( a b s o r p t i o n s ) a n d t o m a i n t a i n i n v e n t o r i e s w i t h a d j u s t m e n t s f o r b o t h c o m p l e t e d a n d u n o c c u p i e d u n i t s and u n i t s u n d e r c o n s t r u c t i o n . O b v i o u s l y , t h i s p a p e r s u p p o r t s t h e u s e o f t h e i n v e n t o r y a p p r o a c h i n t h e h o u s i n g m a r k e t , b u t two c o n c e r n s may l i m i t t h e s u c c e s s o f t h e e m p i r i c a l r e s u l t s . F i r s t , t h e r e i s no c o n c l u s i v e e v i d e n c e t o s u p p o r t t h e a s s u m p t i o n t h a t t h e l e v e l o f u n i t s t a r t s i s t h e most a p p r o p r i a t e m e a sure t o e s t i m a t e c o n s t r u c t i o n a c t i v i t y . I t i s f e a s i b l e t o e x p e c t c o m p l e t i o n s t o r e s p o n d more r a p i d l y t o demand c h a n g e , a n d p r o v i d e an i n d i c a t o r o f new s t o c k . H o w ever, s t a r t s do i n d i c a t e t h e l e v e l o f new c o n s t r u c t i o n a c t i v i t y a n d a s s u m i n g t h a t most u n i t s s t a r t e d a r e c o m p l e t e d , s t a r t s s h o u l d r e f l e c t b o t h demand a n d e c o n o m i c f a c t o r s i n t h e m a r k e t . S e c o n d , m u l t i f a m i l y u n i t s a r e r e p o r t e d a s t h e e n t i r e s t r u c t u r e , t h e r e i s no u n i f o r m s t r u c t u r e s i z e a n d i n d i v i d u a l u n i t s w i t h i n a s t r u c t u r e a r e n o t o c c u p i e d u n t i l t h e e n t i r e s t r u c t u r e i s c o m p l e t e . S u c h i n d i v i s i b i l i t i e s may b i a s t h e a p p l i c a t i o n o f t h e i n v e n t o r y model t o t h e m u l t i f a m i l y h o u s i n g 55 m a r k e t s i n c e i t i s n o t p o s s i b l e t o s t a r t o r c o m p l e t e i n d i v i d u a l u n i t s a s may be d e s i r e d . 56 5. DATA E m p i r i c a l m o d e l s o f t h e h o u s i n g m a r k e t have s u f f e r e d s e v e r e d a t a l i m i t a t i o n s ; f r e q u e n t l y d e s i r e d s e r i e s were u n a v a i l a b l e , i n a d e q u a t e o r i n c o n s i s t e n t . D e s p i t e i m p r o v e m e n t s , t h i s s t u d y i s a l s o c o n s t r a i n e d by t h e f o r m and a v a i l a b i l i t y o f p u b l i s h e d d a t a s e r i e s . T h i s c h a p t e r w i l l b r i e f l y r e v i e w t h e d a t a r e q u i r m e n t s o f t h e m o d e l , t h e r e s p e c t i v e s e r i e s c h o s e n , g e n e r a l t r e n d s i n t h e d a t a a n d how t h e s e s u p p o r t t h e g e n e r a l c o n c e p t o f t h e m o d e l . As p r e v i o u s l y n o t e d , t h e d a t a i s f o r t h e V a n c o u v e r CMA, q u a r t e r l y f rom.1963:1 t o 1982:4. 5.1 MODEL REQUIREMENTS The p r o p o s e d m o d el i s b a s e d on t h e demand f o r r e n t a l u n i t s , and t h e r e s u l t a n t c h a n g e s i n a v a i l a b l e i n v e n t o r i e s a n d s t a r t s o f m u l t i f a m i l y h o u s i n g u n i t s . I d e a l l y , t h e s e d a t a a n d t h e r e s p e c t i v e e c o n o m i c v a r i a b l e s f r o m t h e f u n c t i o n a l e q u a t i o n s w o u l d be a p p l i e d i n t h e e m p i r i c a l a n a l y s i s . The C a n a d i a n C e n s u s , c o n d u c t e d e v e r y f i v e y e a r s , p r o v i d e s t h e most c o m p l e t e a n d r e l i a b l e h o u s e h o l d d a t a , i n c l u d i n g a b r e a k d o w n by t h e t y p e o f a c c o m o d a t i o n ( r e n t a l o r o w n e r s h i p ) a n d age o f t h e h o u s e h o l d h e a d . The e c o n o m i c v e c t o r f o r t h e c h a n g e i n t h e number o f h o u s e h o l d s i n c l u d e s i n c o m e , u n e m p l o y m e n t , r e n t s a n d t h e p r i c e o f h o u s i n g . Income m e a s u r e s a v a i l a b l e f o r t h e e n t i r e t i m e p e r i o d i n c l u d e t h e t o t a l c u r r e n t i ncome p e r month and t h e e s t i m a t e d d i s p o s a b l e i ncome f o r a l l o f B r i t i s h C o l u m b i a . 57 S i m i l a r l y , the only measure of. unemployment i s f o r a l l of B r i t i s h Columbia, from 1966 to 1982. Vancouver's unemployment may be over or understated by t h i s measure, but, i s expected to fol l o w a s i m i l a r t r e n d . Consumer p r i c e indexes are used f o r re n t s , the p r i c e of housing and the p r i c e of other goods and s e r v i c e s . Indexes f o r Vancouver are a v a i l a b l e from 1970; p r i o r to t h i s , the Canadian index have been s u b s t i t u t e d . A b s o r p t i o n s , c a l c u l a t e d as the change i n i n v e n t o r i e s plus completions, are determined from monthly data p u b l i s h e d by CMHC. The independent v a r i a b l e s in t h i s f u n c t i o n a l equation, the change i n r e n t a l households, vacancy r a t e , d e m o l i t i o n s and co n v e r s i o n s , are not as e a s i l y o b t a i n e d . As mentioned above, household data i s only a v a i l a b l e for the census years and must be i n t e r p o l a t e d f o r the i n t e r v e n i n g p e r i o d s . Vacancy r a t e s are a v a i l a b l e from the CHMC survey of m u l t i f a m i l y housing, a n n u a l l y from 1963 to 1969 and semi-annually from 1970 to 1982. Annual d e m o l i t i o n data f o r 1971 to 1981 has been obtained from S t a t i s t i c s Canada, but data from p r e v i o u s years i s u n a v a i l a b l e . F i n a l l y , estimates of con v e r s i o n s and expenditures on con v e r s i o n s are not r e a d i l y a v a i l a b l e i n a form which can be in c o r p o r a t e d i n t o the model s t r u c t u r e . A c t u a l s t a r t s and inventor y f o r each q u a r t e r are r e a d i l y a v a i l a b l e from p u b l i s h e d CMHC data. The d i f f i c u l t y with the d e f i n i t i o n of m u l t i f a m i l y or apartment u n i t s f o r the a v a i l a b l e s e r i e s w i l l be d i s c u s s e d l a t e r . M i s s i n g f o r the e s t i m a t i o n of the supply equations are the d e s i r e d inventory l e v e l and the p r o f i t a b i l i t y of m u l t i f a m i l y investments. Obviously, the 58 f o r m e r c a n n o t be o b t a i n e d , a n d i t i s n e c e s s a r y t o d e r i v e a p r o x y f o r p r o f i t a b i l i t y . P r e v i o u s s t u d i e s ( R o s e n , 1979) h a v e u s e d t h e r e n t a l CPI d e f l a t e d by t h e c o n s t r u c t i o n c o s t CPI o r t h e t o t a l CPI a s a p r o x y . A s i m i l a r f o r m w i l l be u s e d i n t h e e m p i r i c a l s p e c i f i c a t i o n . The Bank R a t e a n d t h e c h a r t e r e d bank p r i m e b u s i n e s s l o a n r a t e have been c o l l e c t e d f o r t h e l a s t Wednesday o f e a c h q u a r t e r . A l t h o u g h i t i s r e c o g n i z e d t h a t t h e r e i s v o l a t i l i t y w i t h i n e a c h q u a r t e r , t h e l a s t o b s e r v a t i o n i s u s e d t o a v o i d t h e d i f f i c u l t i e s w i t h a v e r a g e v a l u e s . B e f o r e e x a m i n i n g t h e s p e c i f i c t r e n d s and d a t a s e r i e s , one g e n e r a l c o n c e r n s h o u l d be a d d r e s s e d , CMA b o u n d a r i e s a n d d a t a d e f i n i t i o n s c h a n g e p e r i o d i c a l l y o r w i t h e a c h c e n s u s . H owever, t h i s c o n c e r n d o e s n o t a f f e c t t h e e m p i r i c a l t e s t s p r e s e n t e d i n t h e . n e x t c h a p t e r . The f o c u s o f t h i s s t u d y i s m u l t i f a m i l y h o u s i n g u n i t s w h i c h a r e l o c a t e d i n t h e u r b a n i z e d a r e a s o f t h e CMA, t h e r e f o r e o v e r t h e s t u d y p e r i o d , t h e number o f m u l t i u n i t s i n s t o c k , s t a r t e d o r i n i n v e n t o r y and t h e number o f m u l t i f a m i l y r e n t a l h o u s e h o l d s a r e n o t be a f f e c t e d by a d j u s t m e n t s i n t h e CMA b o u n d a r i e s . W i t h r e g a r d t o o t h e r c h a n g e s i n d a t a d e f i n i t i o n s , t h e most s i g n i f i c a n t h ave been i n t h e CPI m e a s u r e s a n d i n v e n t o r y . T h e s e w i l l be n o t e d i n t h e r e s p e c t i v e d i s c u s s i o n s o f t h e d a t a t r e n d s . 5.2 POPULATION AND HOUSEHOLDS To d e v e l o p a q u a r t e r l y s e r i e s f o r p o p u l a t i o n and h o u s e h o l d s ( r e n t a l a n d t o t a l ) i t i s n e c e s s a r y t o i n t e r p o l a t e f r o m t h e a v a i l a b l e c e n s u s d a t a . From T a b l e 5.1 i t c a n be n o t e d t h a t t h e T a b l e 5.1 H o u s e h o l d s - V a n c o u v e r CMA Y e a r Age o f S i n g l e A p a r t m e n t Owner R e n t a l T o t a l H s e h o l d D e t a c h e d O c c u p i e d Head 1961 <25 4248 3414 2081 5612 7693 25-34 32650 9834 24798 17812 42610 35-44 44448 7446 38366 1 3626 51 922 45-54 39618 7973 36397 1 1297 47694 55-64 25499 7087 24910 7749 32659 65 + 34000 11876 32862 1 3086 45948 TOTAL 180463 47630 159414 69182 228596 1966 <25 4639 1 0434 2089 13050 15139 25-34 32275 1 6307 23933 24834 48767 35-44 47342 1 1 524 42036 1 6956 58992 45-54 43884 1 1 347 41 277 14103 55380 55-64 29804 1 1 028 29284 1 1691 40975 65 + 33431 19161 32776 1 9927 52703 TOTAL 191375 79802 171395 100561 271956 1 971 <25 7395 1 7380 2620 22325 24945 25-34 41 440 27980 30565 39270 69835 35-44 53995 1 3585 48110 1 9775 67885 45-54 51145 1 4430 47905 18025 65930 55-64 39000 15315 381 1 5 16725 54840 65 + 37060 24975 36295 26145 62440 TOTAL 230030 113665 203615 142260 345870 1 976 <25 1 1 445 20830 4430 281 55 32585 25-34 58255 34630 45260 48435 93695 - 35-44 5581 5 14380 53640 20010 73650 45-54 561 65 15630 54185 18345 72530 55-64 42890 18335 43625 18705 62330 65+ 39155 32470 41000 31780 72780 TOTAL 266720 136285 242130 165430 407560 S o u r c e : S t a t i s t i c s C a n a d a , C e n s u s R e p o r t s 60 number of households i s i n c r e a s i n g but the t o t a l percentage demanding r e n t a l accomodation i s r e l a t i v e l y s t a b l e . However, changes w i t h i n the age c o h o r t s can be noted. To i n t e r p o l a t e r e n t a l demand from these data using a s t r a i g h t l i n e t rend assumes that the p o p u l a t i o n or number of households are growing at a c o n s t a n t . r a t e . A more accurate p o p u l a t i o n s e r i e s c o u l d be d e r i v e d from b i r t h , death and m i g r a t i o n data, but, t h i s would not i n c o r p o r a t e household formation, or the tenure d e c i s i o n s of these households. C l e a r l y , i t i s not p o s s i b l e to estimate an equation f o r q u a r t e r l y changes i n the number of households. However, i n c o n s i d e r i n g the demand f o r r e n t a l u n i t s and the a b s o r p t i o n of new m u l t i f a m i l y u n i t s , some estimate of r e n t a l households i s needed. As d i s c u s s e d w i t h i n the model, t h i s demand may be the r e s u l t of demographic or non-demographic change. To c a l c u l a t e the number of new r e n t a l households a t t r i b u t a b l e to the demographic s t r u c t u r e of the p o p u l a t i o n , i t i s assumed that the headship r a t e s and the percentage of apartment d w e l l e r s f o r each age cohort w i l l remain c o n s t a n t . To be c o n s i s t e n t with other data s e r i e s where 1971 i s the base year (CPl i n d i c i e s ) , the headship r a t e s and r e n t a l r a t e s f o r 1971 were chosen as the base. Using p o p u l a t i o n data from each census i t i s p o s s i b l e to develop an estimate of new r e n t a l households i n each q u a r t e r . (see Appendix A) By e l i m i n a t i n g the demographic demand, any a d d i t i o n a l changes i n the number of new r e n t a l households may be a t t r i b u t e d to economic f a c t o r s , as proposed i n the m o d e l . 1 6 61 A s e c o n d component o f demand i s m i g r a t i o n f o r w h i c h n e t f a m i l y a l l o w a n c e t r a n s f e r s i n B r i t i s h C o l u m b i a a r e u s e d a s a p r o x y . The d i f f i c u l t y w i t h s u c h a s e r i e s i s t w o f o l d . F i r s t , i t w i l l n o t a c c o u n t f o r m i g r a t i o n w i t h i n t h e p r o v i n c e w h i c h may be a m a j o r f a c t o r i n V a n c o u v e r . S e c o n d , f a m i l y a l l o w a n c e t r a n s f e r s do n o t r e c o r d t h e movement o f s i n g l e p e r s o n h o u s e h o l d s , o r h o u s e h o l d s w i t h o u t c h i l d r e n . T h e s e two s e g m e n t s w i l l h ave t h e g r e a t e s t i m p a c t on t h e r e n t a l m a r k e t . However, i n C a n a d a , t h e r e a r e no o t h e r m i g r a t i o n s e r i e s a v a i l a b l e , so t h i s s e r i e s i s u s e d a s t h e b e s t p r o x y of h o u s e h o l d movement. 5.3 C P l INDEXES R e n t a l c o s t s , t h e p r i c e o f h o u s i n g , c o n s t r u c t i o n c o s t s and t h e p r i c e o f o t h e r goods a n d s e r v i c e s a r e r e q u i r e d i n e s t i m a t i n g t h e demand f o r new r e n t a l u n i t s a n d e s t i m a t i n g t h e p r o f i t a b i l i t y o f c o n s t r u c t i o n . The most commonly u s e d s e r i e s a r e t h e C P l i n d e x e s a s r e p o r t e d m o n t h l y by S t a t i s t i c s C a n a d a . T h e s e a r e a v a i l a b l e f o r t h e r e q u i r e d m e a s u r e s , h o w e v e r , some a d j u s t m e n t s were n e c e s s a r y . The C P l i n d e x e s a r e U p d a t e d p e r i o d i c a l l y t o r e f l e c t c h a n g e s i n t h e c o n s u m e r ' b a s k e t o f g o o d s ' a n d t h e b a s e y e a r . The ' b a s k e t o f g o o d s ' c h a n g e s a r e t o e n s u r e t h a t t h e i n d e x r e f l e c t s t y p i c a l c o n s u m p t i o n p a t t e r n s a n d c o n s e q u e n t l y s h o u l d n o t g e n e r a t e any c o n c e r n f o r t h i s s t u d y . The a d j u s t m e n t o f t h e b a s e y e a r f r o m 1949 t o 1961 a n d a g a i n t o 1971 r e q u i r e s t h a t t h e r e l e v a n t s e r i e s be a d j u s t e d t o a common b a s e . The s e r i e s were a l l a d j u s t e d t o r e f l e c t 1971 a s t h e b a s e y e a r . 1 7 F o r a l l o f t h e 62 C P l s e r i e s , e x c e p t t h e V a n c o u v e r t o t a l C P l , p r i o r t o 1970, d a t a was n o t c o l l e c t e d on a r e g i o n a l b a s i s . I t was, t h e r e f o r e , n e c e s s a r y t o s u b s t i t u t e t h e C a n a d i a n d a t a f o r t h e s e m i s s i n g v a l u e s . T h i s s u b s t i t u t i o n s h o u l d n o t c r e a t e any d i f f i c u l t y i n t h e a n a l y s i s s i n c e p l o t s o f t h e s e r i e s i n d i c a t e t h a t t h e g e n e r a l t r e n d s a r e s i m i l a r and t h e m o d e l d o e s n o t r e q u i r e a c o m p a r i s o n o f V a n c o u v e r a n d C a n a d i a n r a t e s . One o f t h e a r g u m e n t s t o e x p l a i n t h e d e c l i n e i n m u l t i f a m i l y c o n s t r u c t i o n i s t h e " r e n t - c o s t s q u e e z e " , d e c r e a s i n g t h e p r o f i t a b i l i t y o f i n v e s t m e n t s i n t h e r e n t a l m a r k e t . E x a m i n a t i o n of t h e r e n t a l component o f t h e C P l , t h e c o n s t r u c t i o n c o s t i n d e x and t h e t o t a l C P l s u p p o r t t h i s h y p o t h e s i s ( s e e A p p e n d i x B ) . The i n c r e a s e s i n r e n t s a r e c l e a r l y l e s s t h a t t h o s e e x p e r i e n c e d i n t h e o t h e r s e r i e s . F u r t h e r , i f r e n t s a r e d e c l i n i n g w i t h r e s p e c t t o o t h e r g o o d s ( i e , r e a l r e n t s a r e d e c l i n i n g ) t h e n t h e demand f o r r e n t a l u n i t s s h o u l d be i n c r e a s i n g . P r e s u m a b l y t h i s w o u l d r e s u l t i n p r i c e i n c r e a s e s u n t i l t h e m a r k e t r e a c h e d a new e q u i l i b r i u m . However t h e p e r s i s t e n t d e c l i n e i n r e a l r e n t s ( b e f o r e and d u r i n g r e n t c o n t r o l s ) t o g e t h e r w i t h l o w v a c a n c i e s s u p p o r t s t h e e x p e c t a t i o n t h a t o t h e r m a r k e t f o r c e s n e e d t o be c o n s i d e r e d . 5.4 STARTS/INVENTORIES I n t h e d e v e l o p m e n t o f t h e t h e o r e t i c a l m o d e l , t h e r e l e v a n t m e a sure o f m u l t i f a m i l y u n i t s was d e f i n e d a s , p r i v a t e l y i n i t i a t e d r e n t a l d w e l l i n g s i n s t r u c t u r e s o f g r e a t e r t h a n two 63 u n i t s ( e x c l u d i n g row h o u s i n g ) . T h i s d e f i n i t i o n e x c l u d e s c o n d o m i n i u m u n i t s a n d g o v e r n m e n t h o u s i n g p r o j e c t s . D a t a p r o v i d e d by CMHC on h o u s i n g d i s t i n g u i s h e s b e t w e e n s i n g l e s , d o u b l e , row, a p a r t m e n t a n d m o b i l e u n i t s , b u t t h e r e i s no d i s t i n c t i o n w i t h i n t h e s e f o r t e n u r e o r t h e s o u r c e c o n s t r u c t i o n f u n d s ( p r i v a t e o r p u b l i c ) . C o n s e q u e n t l y , t h e b e s t c o n s i s t e n t s e r i e s a v a i l a b l e i s t h e number o f a p a r t m e n t u n i t s s t a r t e d , c o m p l e t e d , i n i n v e n t o r y a n d a b s o r b e d where a p a r t m e n t u n i t s i n c l u d e : d o u b l e d u p l e x e s , t r i p l e x e s , row d u p l e x e s , a p a r t m e n t s and d w e l l i n g s o v e r o r a t t h e back o f n o n - r e s i d e n t i a l s t r u c t u r e s . 1 8 F u r t h e r , t h e s e w i l l i n c l u d e p r i v a t e u n i t s a n d u n i t s r e c e i v i n g any f o r m o f g o v e r n m e n t a s s i s t a n c e . S i n c e 1970, t h e g o v e r n m e n t h a s t a k e n a more a c t i v e r o l e i n t h e h o u s i n g m a r k e t . , P r i o r t o t h i s t i m e , i t i s e x p e c t e d . t h a t t h e go v e r n m e n t i n v o l v e m e n t w o u l d n o t h a v e s i g n i f i c a n t l y a l t e r e d t h e r e s u l t s . I n 1982, CMHC s t a r t e d t o c o l l e c t m u l t i f a m i l y h o u s i n g d a t a a c c o r d i n g t o s o u r c e o f f u n d s ( p r i v a t e o r p u b l i c ) a s w e l l a s t h e t y p e o f s t r u c t u r e . T a b l e s 5.2 a n d 5.3 p r e s e n t t h e m o n t h l y s t a r t s a n d c o m p l e t i o n s f o r V a n c o u v e r i n 1982. M a r k e t r e n t a l u n i t s r a n g e f r o m l e s s t h a n 10 p e r c e n t o f t o t a l s t a r t s t o g r e a t e r t h a n 90 p e r c e n t . W i t h t h i s v o l a t i l i t y i n t h e s t r u c t u r e o f t h e s t a r t s s e r i e s , i t i s i m p o s s i b l e t o u s e t h i s d a t a t o e s t i m a t e p r e v i o u s n o n - m a r k e t r e n t a l s t a r t s i n p r e v i o u s y e a r s . H o w e v e r , t h e two s e g m e n t s do a p p e a r a n t i c y c l i c a l . G o v e r n m e n t h o u s i n g p r o j e c t s may r e s u l t i n a s m o o t h e r s t a r t s s e r i e s t h a n w o u l d e x i s t w i t h o n l y p r i v a t e l y i n i t i a t e d u n i t s . As a s e c o n d i n d i c a t o r o f g o v e r n m e n t i n v o l v e m e n t , a p p r o v a l s 64 T a b l e 5.2 M a r k e t and I Non M a r k e t H o u s i n g S t a r t s V a n c o u v e r 1982 M o n t h Non : P r o f i t R e n t Co op T o t a l Non M a r k e t M a r k e t Ren Row A p t Row A p t Row A p t Row A p t J a n 68 1 4 90 0 158 14 4 291 F e b 0 38 0 223 0 261 0 338 Mar 33 78 0 0 33 78 48 492 A p r 0 0 305 101 305 101 15 750 May 41 18 56 63 97 81 8 226 J u n 88 76 71 0 159 76 0 188 J u l 30 0 24 1 70 54 1 70 0 39 Aug 36 20 34 99 70 119 0 86 Sep 57 199 40 0 97 199 51 81 Oct 0 0 0 92 0 92 0 54 Nov 36 40 38 0 74 40 54 4 Dec 52 42 61 28 1 13 70 72 148 TOTAL 441 525 719 776 1 160 1301 252 2697 S o u r c e : u n p u b l i s h e d CMHC F i l e s , V a n c o u v e r R e g i o n a l O f f i c e 65 T a b l e 5.3 M a r k e t and Non M a r k e t H o u s i n g C o m p l e t i o n s V a n c o u v e r 1982 M o n t h Non ] P r o f i t R e n t Co op T o t a l Non M a r k e t M a r k e t R ent Row A p t Row A p t Row A p t Row A p t J a n 0 0 14 0 14 0 1 1 2 101 F e b 0 41 188 1 54 188 195 1 4 668 Mar 0 85 91 0 91 85 91 299 A p r 83 66 13 0 96 66 205 431 May 0 67 0 0 0 67 50 573 J u n 0 66 0 1 1 2 0 178 74 359 J u l 1 06 75 0 1 1 1 1 06 186 1 20 430 Aug 96 183 1 66 30 262 213 22 327 Sep 101 92 196 152 297 244 98 472 O c t 183 18 58 13 241 31 40 168 Nov 86 53 76 0 1 62 53 28 342 Dec 30 0 172 88 202 88 43 700 TOTAL 685 746 974 660 1 659 1 406 814 4870 ' S o u r c e : u n p u b l i s h e d CMHC F i l e s , V a n c o u v e r R e g i o n a l O f f i c e 66 of s o c i a l housing p r o j e c t s from 1968 to 1983 were examined (see Table 5.4). These are given by the date of the p r o j e c t approval by CMHC and t h e r e f o r e do not correspond d i r e c t l y with the s t a r t s s e r i e s and cannot be used to ad j u s t the s t a r t s s e r i e s to remove government housing. However, the l a r g e number of approvals i n 1974 through 1976 and again i n 1980 and 1981 support the ex p e c t a t i o n that government p r o j e c t s w i l l d i s t o r t the data and p o s s i b l y the r e s u l t s . P r i o r to 1966, i t was not p o s s i b l e to own a m u l t i f a m i l y housing u n i t . I n t r o d u c t i o n of s t r a t a t i t l e s i n c r e a s e d the complexity of the m u l t i f a m i l y housing market. B u i l d i n g s c o u l d be r e g i s t e r e d with a s t r a t a t i t l e upon completion and s o l d as condominium u n i t s . Or, u n i t s i n the e n t i r e b u i l d i n g c o u l d be maintained by one owner and the i n d i v i d u a l u n i t s rented. Or, the i n d i v i d u a l u n i t s c o u l d be s o l d and then rented by the i n d i v i d u a l owners or the b u i l d i n g maintained by a management company. The a b i l i t y to change to ownership from r e n t a l , or v i s v e r s a , i n c r e a s e s the d i f f i c u l t y i n d e f i n i n g the m u l t i f a m i l y housing s t o c k . A l s o , these u n i t s are not i n c l u d e d i n the vacancy survey, suggesting p o t e n t i a l f o r the vacancy rate to be underestimated. Data i s c u r r e n t l y being c o l l e c t e d to d i s t i n g u i s h r e n t a l and condominium u n i t s upon s t a r t and completion. Since tenure can change a f t e r completeion, such data w i l l not a l l e v i a t e f u l l y the d i f f i c u l t i e s i n d e f i n i n g the r e n t a l s tock. Despite these shortcomings, CMHC pr o v i d e s the best measure of housing u n i t s t a r t s , completions, i n v e n t o r i e s and vacancy r a t e s . 67 T a b l e 5.4 S o c i a l H o u s i n g P r o j e c t A p p r o v a l s V a n c o u v e r Y e a r Q t r U n i t s Y e a r Q t r U n i t s Y e a r Q t r U n i t s 1968 1 0 1974 1 583 1980 1 0 2 121 2 0 2 0 3 59 3 0 3 0 4 69 4 1002 4 1756 1 969 1 1 74 1975 1. 0 1 981 1 0 2 0 2 0 2 0 3 0 3 0 3 0 4 699 4 1214 4 1616 1970 1 86 1976 1 0 1 982 1 129 2 0 2 0 2 0 3 0 3 0 3 0 4 586 4 1 508 4 1 1 38 1 971 1 0 1977 1 0 1 983 1 419 2 0 2 0 2 0 3 0 3 0 3 0 4 805 4 1 38 4 370 1972 1 19 1978 1 0 2 0 2 0 3 0 3 0 4 487 4 264 1973 1 1 63 1979 1 69 2 0 2 0 3 0 3 0 •„ 4 322 4 83 S o u r c e : CMHC, B.C. and Yukon R e g i o n a l O f f i c e , S p e c i a l R e p o r t 68 S t a r t s f o r m u l t i f a m i l y h o u s i n g a r e r e c o r d e d when t h e f o o t i n g h a s been i n s t a l l e d , a c c o r d i n g t o t h e number o f u n i t s r e c o r d e d on t h e s t r u c t u r e p l a n s a n d t h e b u i l d i n g p e r m i t a p p l i c a t i o n . T h e r e i s c l e a r l y room f o r e r r o r i n r e c o r d i n g b o t h t h e t i m i n g o f t h e s t a r t a n d t h e number o f u n i t s w h i c h w i l l be c o n s t r u c t e d . The e x t r e m e v o l a t i l i t y i n s t a r t s i s e v i d e n t i n F i g u r e 5.1, a l t h o u g h t h e r e i s some s e a s o n a l i t y i n t h e s e r i e s . S i n c e t h e peak i n 1969, c o n s t r u c t i o n o f m u l t i f a m i l y h o u s i n g u n i t s h a s b een d e c l i n i n g , w i t h a s u d d e n i n c r e a s e i n 1981 i n r e s p o n s e t o t h e r e m o v a l o f t h e t a x b e n e f i t s f o r m u l t i f a m i l y d w e l l i n g s ( a s o f December 31 , 1 9 8 1 ) . U n i t s u n d e r c o n s t r u c t i o n a r e e x p e c t e d t o l a g s t a r t s , a n d s h o u l d , by d e f i n i t i o n , e q u a l p r e v i o u s u n i t s u n d e r c o n s t r u c t i o n p l u s s t a r t s i n t h e c u r r e n t p e r i o d , l e s s c o m p l e t i o n s . H o w e v e r , t h i s d e f i n i t i o n d o e s n o t f i t p r e c i s e l y s i n c e t h i s s e r i e s i s u s e d t o a c c o u n t f o r any n e c e s s a r y a d j u s t m e n t s . I f c o n s t r u c t i o n c e a s e s a f t e r a s t a r t h a s been r e c o r d e d , o r i f upon c o m p l e t i o n a s t r u c t u r e c o n t a i n s f e w e r o r more u n i t s t h a n r e p o r t e d a s s t a r t s , a d j u s t m e n t s a r e r e c o r d e d i n t h e number o f u n i t s u n d e r c o n s t r u c t i o n . No c o r r e c t i o n s a r e made t o t h e o t h e r d a t a s e r i e s i n v o l v e d . A c o m p l e t i o n i s r e c o r d e d when a l l o f t h e p r o p o s e d c o n s t r u c t i o n work on t h e s t r u c t u r e h a s b e e n c o m p l e t e d . F o r m u l t i f a m i l y u n i t s t h i s i n c l u d e s t h e e n t i r e s t r u c t u r e , n o t i n d i v i d u a l u n i t s . C o n s e q u e n t l y , c o m p l e t i o n s s h o u l d l a g s t a r t s ( s e e F i g u r e 5 . 2 ) , b u t i t i s d i f f i c u l t t o d e f i n e t h e p r e c i s e l a g s t r u c t u r e s i n c e t h e s i z e o f s t r u c t u r e w i l l i n f l u e n c e t h e Figure 5.1 VANCOUVER QUARTERLY MULTI FAMILY HOUSING STARTS U n i t s 4,000 I. 3,000 \- 2,000 k 1,000 b 1964 U966 1968 1970 1972 1974 1976 1978 1980 Figure 5.2 VANCOUVER QUARTERLY MULTI FAMILY HOUSING COMPLETIONS J I I I I L 1 9 6 4 1 9 6 6 1 9 6 8 J 1 I I I L 1 9 7 0 1 9 7 2 1 9 7 4 i l 9 7 6 J ' 1 9 7 8 WO* W 71 c o n s t r u c t i o n h o r i z o n and l a r g e s t r u c t u r e s may d i s t o r t the appearance of the data. A r e g r e s s i o n of completions on s t a r t s lagged up to one year i n d i c a t e s the b a s i c s t r u c t u r e of these two s e r i e s (see Table 5.5). The r e l a t i v e l y low R 2 f o r two s e r i e s which should be h i g h l y c o r r e l a t e d i s d i s t u r b i n g . As expected, s t a r t s i n the cu r r e n t quarter are i n s i g n i f i c a n t . The other c o e f f i c i e n t s suggest that completions l a g s t a r t s by 6 months to a year. C l e a r l y , the p r o j e c t s i z e w i l l i n f l u e n c e the c o n s t r u c t i o n time. A l s o , i f a b s o r p t i o n s decrease, b u i l d e r s may delay or h a l t c o n s t r u c t i o n u n t i l demand warrants c o n t i n u a t i o n . Since p r o j e c t s i z e and delays cannot be determined, these r e s u l t s are not alarming and do not i n d i c a t e e r r o r s i n the r e s p e c t i v e s e r i e s . I n v e n t o r i e s are u n i t s completed and not yet occupied (see Fi g u r e 5.3). P r i o r to 1970, unoccupied u n i t s were recorded as inventory f o r s i x months; i f the u n i t s were s t i l l unoccupied a f t e r s i x months, the u n i t s were i n c l u d e d i n the vacancy r a t e survey. In 1979 t h i s was i n c r e a s e d to 12 months, and f u r t h e r i n c r e a s e d to 36 months i n 1982. By d e f i n i t i o n , a b s o r p t i o n s are those u n i t s from e x i s t i n g i n v e n t o r i e s or newly completed u n i t s which are occupied or rented i n the p e r i o d . T h i s s e r i e s i s not p u b l i s h e d , but has been d e r i v e d from the above data (see F i g u r e 5.4). Vacancy r a t e s i n d i c a t e the percentage of u n i t s i n the e x i s t i n g stock which are a v a i l a b l e f o r r e n t . T h i s i n f o r m a t i o n i s a v a i l a b l e a n n u a l l y from 1963 to 1970 and semi-annually a f t e r 1970 (see Table 5.6). To expand the s e r i e s t o q u a r t e r l y data, a Table 5.5 Regression for Completions with Lagged Starts Lagged Starts Constant . 0 •1 -2 -3 -4 R« R1 SE 304.92 -0. 028 0. 194 O .316 0 035 0 .223 0 .455 0.4 16 461.40 6 (0. .361 ) (2. 285) (3 .682) (0. . 408 ) (2 .757) 460.92 -O. .012 0. 202 0. .345 0 112 _ 0. 396 0. 362 482.38 5 (0. . 146) (2. 272) (3 .876) (1. 343) 284.76 _ 0. 183 0 .312 0. 034 0. . 221 0. 454 O r423 458.57 1 (2. 316) (3. 687) (0. 406) (2. 755) 451.68 _ 0. 197 0. 343 0. 112 - 0. 396 O. 370 479.09 O (2. 387) (3. 912) (1. 347) Notes: (1) t-stat1st1cs In parenthesis (2) R' values reported are: f i r s t the unadjusted R', and second the adjusted R' (3) SE denotes the standard error (4) DW denotes the Durbin-Watson s t a t i s t i c Figure 5.3 VANCOUVER QUARTERLY MULTI FAMILY HOUSING INVENTORY Units 4,000 3,000 2,000 1,000 I I * • « • « • I I I L. 1 1 1 1 1 1 1 1 1964 1966 1968 1970 1972 1974 1976 1978 1 980, 1982 Figure 5.4 VANCOUVER QUARTERLY MULTI FAMILY HOUSING ABSORPTION Units 4^000 3,000 2,000 1,000 • i t i I I i i • t i i 1 1 — — i 1 1 1 —I 1 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 T a b l e 5.6 V a n c o u v e r V a c a n c y R a t e s Y e a r R a t e 1963 4 .2 1964 4 .7 1965 4 .0 1966 1 .5 1967 1 .0 1968 1 .3 1969 1 .2 1 9 7 0 ( J u n e ) 2 .7 (Dec) 2 . 1 1 9 7 1 ( J u n e ) 4 . 1 (Dec) 2 .8 l 9 7 2 ( J u n e ) 2 .4 (Dec) 0 .6 1 9 7 3 ( J u n e ) 1 .0 (Dec) 0 .4 l 9 7 4 ( J u n e ) 0 .3 (Dec) 0 . 1 Y e a r R a t e l 9 7 5 ( A p r ) 0.2 ( O c t ) 0.1 1 9 7 6 ( A p r ) 0.4 ( O c t ) 0.7 1 9 7 7 ( A p r ) 1 .6 ( O c t ) 1 .6 1 9 7 8 ( A p r ) 1 .5 ( O c t ) 1 .4 1 9 7 9 ( A p r ) 0.9 ( O c t ) 0.2 1 9 8 0 ( A p r ) 0.1 ( O c t ) 0.1 1 9 8 1 ( A p r ) 0.1 ( O c t ) 0.1 1 9 8 2 ( A p r ) 0.6 ( O c t ) 1.9 S o u r c e : Canada M o r t g a g e and H o u s i n g C o r p o r a t i o n , v a c a n c y s u r v e y 76 s t r a i g h t t r e n d b e t w e e n p e r i o d s was assumed. T h i s may i n t r o d u c e some e r r o r , b u t c h a n g e s i n t h e s e r i e s a r e r e l a t i v e l y s m o o t h , so i t i s a n t i c i p a t e d t h a t any e r r o r w o u l d be m i n i m a l . The f i n a l s t o c k s e r i e s c o l l e c t e d was d e m o l i t i o n s . T h e s e were a v a i l a b l e a n n u a l l y f r o m 1971 t o 1981 ( s e e T a b l e 5 . 7 ) . I t may be p o s s i b l e t o p r e p a r e a m o v i n g a v e r a g e s e r i e s f r o m t h e a n n u a l d a t a t o a p p r o x i m a t e t h e q u a r t e r l y s e r i e s . However,, t h e g a i n f r o m t h i s was n o t s e e n a s s i g n i f i c a n t a n d t h e s e have n o t been i n c l u d e d i n t h e f i n a l m o d e l . 5.5 A P P L I C A T I O N TO THE MODEL B r i e f l y , w i t h i n t h e p r o p o s e d m o d e l , t h e f o l l o w i n g d a t a w i l l be u s e d . 1 9 The c h a n g e i n r e n t a l h o u s e h o l d s f r o m d e m o g r a p h i c f a c t o r s i s e s t i m a t e d u s i n g h e a d s h i p r a t e s a n d t h e p e r c e n t a g e o f r e n t a l h o u s e h o l d s i n 1971 a s a b a s e . F a m i l y a l l o w a n c e t r a n s f e r s a r e u s e d a s a p r o x y f o r m i g r a t i o n . The e c o n o m i c v e c t o r o f v a r i a b l e s a f f e c t i n g n o n - d e m o g r a p h i c c h a n g e w i l l i n c l u d e t h e d i s p o s a b l e income f o r B r i t i s h C o l u m b i a ( i n c o n s t a n t 1971 d o l l a r s ) , t h e r e p o r t e d unemployment r a t e f o r B r i t i s h C o l u m b i a and t h e r e n t a l component o f t h e C P l . A b s o r p t i o n s a r e c a l c u l a t e d f r o m t h e i n v e n t o r y a n d c o m p l e t i o n s d a t a r e p o r t e d by CMHC. The v a c a n c y r a t e i s e x p a n d e d f r o m t h e v a c a n c y s u r v e y c o n d u c t e d by CMHC. S i n c e t h e r e a r e no c o n s i s t e n t s e r i e s f o r d e m o l i t i o n s a n d c o n v e r s i o n s , t h e s e i m p a c t s c a n n o t be e x p l i c i t l y m o d e l l e d . S t a r t s , c o m p l e t i o n s a n d i n v e n t o r y a r e a v a i l a b l e a s t h e number o f a p a r t m e n t u n i t s f o r e a c h p e r i o d . The d e f i n i t i o n o f a p a r t m e n t i n c l u d e s c o n d o m i n i u m s a n d g o v e r n m e n t h o u s i n g p r o j e c t s T a b l e 5.7 V a n c o u v e r H o u s i n g U n i t D e m o l i t i o n P e r m i t s Y e a r S i n g l e s D o u b l e s 1 971 789 41 1972 819 32 1973 1238 71 1974 1312 70 1975 930 21 1976 1 334 57 1977 1 287 51 1978 1181 61 1979 1 025 27 1980 1592 93 1 981 1777 91 Row A p t T o t a l - 161 991 - 115 966 12 299 1618 - 182 1564 -• 119 1070 - 1 18 1509 - 1 39 1 477 - 241 1483 - 1 46 1 198 63 501 2249 6 403 2277 S o u r c e : S t a t i s t i c s C a n a d a , S p e c i a l R e p o r t 78 w h i c h i s i n c o n s i s t e n t w i t h t h e t h e o r e t i c a l d e f i n i t i o n . P r o f i t s w i l l be e s t i m a t e d as t h e r e n t a l C P l , d e f l a t e d by t h e r e s i d e n t i a l c o n s t r u c t i o n c o s t C P l . T h e s e m e a s u r e s a r e c o n s i s t e n t w i t h e s t i m a t e s u s e d i n most o f t h e r e s e a r c h a s a c o n s i s e , a c c u r a t e p r o f i t m e a s u r e f o r m u l t i f a m i l y h o u s i n g u n i t s d o e s n o t e x i s t . The i n t e r e s t r a t e m e a s u r e most c o n s i s t e n t w i t h c o n s t r u c t i o n l o a n s w i l l be t h e Bank R a t e . The e x p e c t e d p a t t e r n s o f t h e s t o c k v a r i a b l e s ( s t a r t s , i n v e n t o r y , a b s o r p t i o n s , v a c a n c y r a t e s ) were o u t l i n e d i n t h e p r e v i o u s c h a p t e r . F o r t h e a c t u a l s e r i e s , t h e s e p a t t e r n s a r e n o t a s w e l l d e f i n e d ( s e e F i g u r e 5.5), b u t some o f t h e e x p e c t e d t r e n d s c a n be n o t e d . S t a r t s do d e c l i n e a f t e r p e r i o d s o f h i g h i n v e n t o r i e s . C o n v e r s e l y , s t a r t s a r e l o w e r when i n v e n t o r y l e v e l s a r e i n c r e a s e d . O b v i o u s l y , t h e t r e n d s do n o t e x a c t l y m a t c h t h e t h e o r e t i c a l m o d e l a n d do n o t a c c o u n t f o r c h a n g e s i n t h e d e s i r e d i n v e n t o r y l e v e l s o r t h e a b i l i t y o f t h e m a r k e t t o a d j u s t t h r o u g h o t h e r m e c h a n i s m s . H o w e v e r , t h e t r e n d s i n t h e a v a i l a b l e d a t a s u p p o r t t h e a p p l i c a t i o n o f an i n v e n t o r y a d j u s t m e n t m o d e l . Units 4,000 3,000 h 2,000 1,000 Figure 5.5 VANCOUVER INVENTORY ADJUSTMENT STARTS INVENTORY ABSORPTIONS starts inventory absorptions 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 80 6. EMPIRICAL ANALYSIS AND TESTING B a s e d on t h e a v a i l a b l e d a t a f o r m u l t i f a m i l y h o u s i n g , t h e e m p i r i c a l a n a l y s i s w i l l c o n s i s t o f t h r e e p a r t s : a s t r u c t u r a l m o d e l d e s i g n e d w i t h i n t h e p r o p o s e d t h e o r e t i c a l m o d e l a n d t h e c o n s t r a i n t s i m p o s e d by t h e a v a i l a b l e d a t a ; a t i m e s e r i e s m o d e l f o r m u l t i f a m i l y h o u s i n g . s t a r t s ; a n d t e s t i n g o f t h e s e two m o d e l s . The f o c u s o f t h i s p a p e r i s on t h e r e s u l t s o f t h e s t r u c t u r a l m o d e l . However, t h e t i m e s e r i e s m o d el i s o f f e r e d a s a m e a sure t o e v a l u a t e t h e p e r f o r m a n c e o f t h e s t r u c t u r a l m o d e l , w i t h i n and o u t s i d e t h e e s t i m a t i o n p e r i o d . The s t r u c t u r a l m o d e l w i l l be e s t i m a t e d t h r o u g h m u l t i p l e r e g r e s s i o n and t h e t i m e s e r i e s w i t h a B o x - J e n k i n s a u t o r e g r e s s i v e - i n t e g r a t e d - m o v i n g a v e r a g e (ARIMA) m o d e l . Q u a r t e r l y d a t a f r o m 1963:1 t o 1980:4 w i l l be u s e d f o r t h e m o d e l e s t i m a t i o n s a n d d a t a f o r 1981:1 t o 1982:4 w i l l be m a i n t a i n e d t o t e s t t h e r e s u l t s a n d t h e f o r e c a s t i n g a b i l i t y o f t h e s e m o d e l s . 6.1 EMPIRICAL MODEL AND ANALYSIS The p r e v i o u s c h a p t e r o u t l i n e d t h e a v a i l a b l e d a t a a n d how t h e s e c o u l d be i n c o r p o r a t e d i n t o t h e p r o p o s e d m o d e l . C l e a r l y , t o f u l l y d e v e l o p t h e s p e c i f i e d t h e o r e t i c a l m o d e l w i t h t h e a v a i l a b l e d a t a s e r i e s w o u l d be e x t e n d i n g t h e d a t a f a r b e y o n d i t s c a p a b i l i t i e s , l e a d i n g t o r a t h e r d u b i o u s r e s u l t s . T h e r e f o r e , t h e e m p i r i c a l m o d e l w i l l c o n s i s t o f two e q u a t i o n s ; t h e f i r s t t o e s t i m a t e t h e a b s o r p t i o n o f new r e n t a l ( m u l t i f a m i l y ) u n i t s a n d 81 t h e s e c o n d , t h e l e v e l o f u n i t s s t a r t s i n a g i v e n q u a r t e r . The a b s o r p t i o n e q u a t i o n w i l l be e s t i m a t e d w i t h t h e e c o n o m i c _ v a r i a b l e s s p e c i f i e d f o r h o u s e h o l d f o r m a t i o n , t h e e x p e c t e d new r e n t a l h o u s e h o l d s f r o m d e m o g r a p h i c c h a n g e a n d m i g r a t i o n . S t a r t s w i l l be e s t i m a t e d u s i n g p r e d i c t e d a b s o r p t i o n s , i n v e n t o r y , a p r o f i t p r o x y and i n t e r e s t r a t e s . Dummy v a r i a b l e s f o r t h e r e s p e c t i v e demand and s u p p l y s i d e g o v e r n m e n t p r o g r a m s a r e p r o p o s e d t o remove t h e i m p a c t s o f g o v e r n m e n t i n t e r v e n t i o n i n t h e h o u s i n g m a r k e t . G i v e n t h e a v a i l a b l e d a t a a n d m o d el s t r u c t u r e , T a b l e s 6.1 a n d 6.2 p r e s e n t t h e v a r i a b l e s and t h e i r e x p e c t e d s i g n i n e a c h e q u a t i o n . An e x a m i n a t i o n o f t h e d a t a r e v e a l e d o b v i o u s t i m e t r e n d s f o r s e v e r a l o f t h e s e r i e s , i n c r e a s i n g t h e l i k e l i h o o d o f m u l t i c o l l i n e a r i t y c r e a t i n g p r o b l e m s i n t h e r e g r e s s i o n a n a l y s i s . P l o t s of t h e d a t a s e r i e s a n d c o r r e l a t i o n a n a l y s i s were u s e d t o d e t e r m i n e w h i c h v a r i a b l e s were most l i k e l y t o c r e a t e s e v e r e e s t i m a t i o n p r o b l e m s . ( s e e A p p e n d i x C) D i s t i n c t t r e n d s a n d h i g h c o r r e l a t i o n s were p r o m i n e n t b e t w e e n t h e i n d e p e n d e n t v a r i a b l e s f o r t h e a b s o r p t i o n e q u a t i o n s , b u t , d i d n o t a p p e a r t o be a c o n c e r n f o r t h e s t a r t s e q u a t i o n . S e v e r a l t e c h n i q u e s a r e a v a i l a b l e t o o v e rcome t h e p r o b l e m of m u l t i c o l l i n e a r i t y , i n c l u d i n g : d i f f e r e n c i n g , s c a l i n g t h e v a r i a b l e s o r t h e s y s t e m a t i c r e m o v a l o f v a r i a b l e s . 2 0 The l a t t e r m e t h o d h a s been a d o p t e d f o r t h i s s t u d y . A b s o r p t i o n s were e s t i m a t e d u s i n g s e v e r a l s p e c i f i c a t i o n s e l i m i n a t i n g v a r i a b l e s w h i c h w ere h i g h l y c o r r e l a t e d o r i n s i g n i f i c a n t . When e n t e r p r e t i n g t h e f i n a l r e s u l t s i t must be n o t e d t h a t t h e o m i s s i o n o f v a r i a b l e s may 82 T a b l e 6.1 V a r i a b l e L i s t F o r A b s o r p t i o n E q u a t i o n V a r i a b l e E x p e c t e d S i g n D e s c r i p t i o n ABSORB ( d e p e n d e n t ) BCFAMALN + DEAPT + BCUR BCURD ? RINC + RRENT RENTMTG RENTRKTG WAC VMFINV + APTSTK ? RCONTR + GRANT AHOP A b s o r p t i o n of new m u l t i f a m i l y u n i t s B.C. f a m i l y a l l o w a n c e t r a n s f e r s ( n e t ) p r o x y f o r m i g r a t i o n E x p e c t e d new r e n t a l h o u s e h o l d s from economic demand B.C. unemployment r a t e Dummy v a r i a b l e f o r m i s s i n g unemployment d a t a (1=1963-1966, 0=1967-1982) R e a l income - B.C. d i s p o s a b l e income R e a l r e n t s - V a n c o u v e r r e n t a l CPI ind e x R a t i o of r e n t i n d e x t o n o m i n a l mortgage r a t e R a t i o of r e n t i n d e x t o r e a l m o r t g a g e r a t e V a n c o u v e r v a c a n c y r a t e f o r r e n t a l m u l t i f a m i l y u n i t s V a n c o u v e r m u l t i f a m i l y i n v e n t o r y (newly c o m p l e t e d and u n o c c u p i e d u n i t s ) E x i s t i n g s t o c k of m u l t i f a m i l y u n i t s Dummy v a r i a b l e f o r r e n t c o n t r o l (0=1963-1973, 1=1974-1982) Dummy v a r i a b l e f o r g r a n t s f o r new home owners (0=1963-1973 & 1976-1982, 1=1974-1975) Dummy v a r i a b l e f o r A s s i s t e d Home O w n e r s h i p Program Q1,Q2,Q3,Q4 Q u a r t e r l y dummy v a r i a b l e s 83 T a b l e 6.2 V a r i a b l e L i s t F o r S t a r t s E q u a t i o n V a r i a b l e E x p e c t e d S i g n D e s c r i p t i o n VMFST ( d e p e n d e n t ) V a n c o u v e r m u l t i f a m i l y u n i t s t a r t s + VMFST1 VMFINV VMFUC V a n v o u v e r m u l t i f a m i l y u n i t s t a r t s l a g g e d one p e r i o d V a n c o u v e r m u l i t f a m i l y u n i t s i n v e n t o r y ( n e w l y c o m p l e t e d a n d u n o c c u p i e d u n i t s ) V a n c o u v e r m u l t i f a m i l y u n i t s u n d e r c o n s t r u c t i o n ABSPRED + PROFIT + BKRAT W A C DUM + MURB + Q1,Q2,Q3,Q4 ? P r e d i c t e d a b s o r p t i o n o f new r e n t a l u n i t s P r o f i t a b i l i t y o f r e n t a l u n i t s ( r e n t C P l i n d e x / c o n s t r u c t i o n c o s t i n d e x ) Bank r a t e on p r i m e b u s i n e s s l o a n s V a n c o u v e r v a c a n c y r a t e f o r r e n t a l m u l t i f a m i l y u n i t s Dummy v a r i a b l e f o r u n u s u a l d a t a 1977,78 ( s e e f o o t n o t e 26) Dummy v a r i a b l e f o r MURB p r o g r a m (0=1973-1974 & 1980, 1=1963-1972 & 1975-1979 & 1981) Q u a r t e r l y dummy v a r i a b l e s 84 r e s u l t i n m i s l e a d i n g c o e f f i c i e n t s f o r the remaining v a r i a b l e s . The s e l e c t i o n of the f i n a l equation was based on the s t a b i l i t y of the c o e f f i c i e n t s , the a d j u s t e d R 2 and the standard e r r o r . The second step of the model development was to estimate an equation f o r m u l t i f a m i l y housing s t a r t s using p r e d i c t e d a b s o r p t i o n s . I t was not necessary to r e s t r u c t u r e the s t a r t s equation to minimize c o r r e l a t i o n between the independent v a r i a b l e s . S e v e r a l s p e c i f i c a t i o n s were t r i e d based on assumptions of the i n c l u s i o n and e x c l u s i o n of u n i t s under c o n s t r u c t i o n and the s i g n i f i c a n c e of the other v a r i a b l e s . A l s o , separate equations were estimated f o r 1963 to 1970 and 1971 to 1980 to determine i f there were s t r u c t u r a l changes in the market based on government i n t e r v e n t i o n and investment d e c i s i o n c r i t e r i a . 6.2 EMPIRICAL RESULTS 6.2.1 A bsorptions In e s t i m a t i n g the a b s o r p t i o n equation, the problem of m u l t i c o l l i n e a r i t y r e s u l t e d i n changes i n the s i g n and magnitude of the c o e f f i c i e n t s . A l t e r n a t e forms of the model t r i e d i n c l u d e d r a t i o s of r e n t s to mortgage c o s t s or ownership c o s t s , r e a l incomes, or e x c l u d i n g other v a r i a b l e s such as demographic change and f a m i l y allowance t r a n s f e r s . The r e s u l t s presented i n Table 6.3 o f f e r the most c o n s i s t e n t model with the best r e s u l t s . As was mentioned, since "some v a r i a b l e s have been omitted t h e i r impacts may be e x p l a i n e d i n the remaining c o e f f i c i e n t s . A l s o , Table 6.3 Regression Results - Absorptions 1963-1980 CONST BCFAMALN DEAPT VMFINV1 VVAC1 BCUR BCURD RRENT APTSTK 01 02 03 GRANT AHOP RCONTR R1 SE/DW 1 . -6289 0 . 143 0 .862 0.652 -26 .63 -128.49 -1172 65.95 0.017 136.31 34.76 -148.05 .570 398 .37 (0 .058) (1 .210) (5.334)(0. 375) (2.002) (2.903)(4 .550)(2.421)(0.792)(0.194) (1.017) .490 1 69 2 . -6063 0. 122 -0. .878 0.636 -130.84 -1251 63 .84 0.017 120.72 14.40 - 160.45 .569 395 .51 (0. .981 ) (1 .260) (5.607) (2.063) (3.670)(4 .695)(2.436)(0.728)(0.085) (1.140) .498 1 .69 3. -8757 0. 347 -1 .294 0.473 -175.26 -1296 82 .30 0.025 352.92 214. 19 -110.19 663.03 420.30 .569 395 .51 (2 478) (1 .996) (3.251) (2.946) (4.138)(5 .887)(3.656)(2.075 ) ( 1 .267 ) ( 1 .267X2.984) (1.588) .498 1 .69 4. -5706 0. 087 -0. 923 0.594 -97.40 -1117 61 .12 0.016 .543 397 . 52 (O. 869) (1. 320) (5.445) ( 1 .654) (3.395)(4 .537X2.230) .492 1 . 70 5. -9075 0. 215 -o. 890 0.595 -123.83 -1179 90 .50 0.019 170.82 81.12 - 137.89 548.3 .589 389 59 (1. 595) (1. 298) (5.208) (1.978) (3.483)(4 365)(2.674)(1.029)(0.473) (0.990) ( 1 .684) .512 1 76 6. -5882 0. 084 -o. 838 0.603 -134. 14 63. 02 0.017 130.89 -11.85 -147.51 .513 416. ,51 (0. 577) (1. 136) (3.941) (1.890) (4. 237)(2. 197)(0.654X0.060) (0.903) .426 1 . 60 Notes: (1) t - s t a t l s t l c s In parenthesis (2) a '1' a f t e r the variable name Indicates that the variable Is lagged one period (3) R' values reported are: f i r s t the unadjusted R'. and second the adjusted R* (4) SE/DW denotes the standard error and Durbln-Watson s t a t i s t i c (5) Equation 2 Is used to estimate absorptions for the st a r t s analysis (6) Equation 6 uses only data from 1966 to 1980 00 86 the downward trend i n a b s o r p t i o n s may be p a r t i a l l y e x p l a i n e d i n those v a r i a b l e s p o r t r a y i n g s i m i l a r (or opposite) t r e n d s . T h e r e f o r e , i n t e r p r e t a t i o n of the c o e f f i c i e n t s may be m i s l e a d i n g , but, i t i s emphasized that t h i s i s not c r i t i c a l to the a n a l y s i s of the s t a r t s e q uation. The f i n a l a b s o r p t i o n equation (Equation 2, Table 6.3) has an a d j u s t e d R 2 of approximately 0.5 and a standard e r r o r of j u s t under 400 (25% of the mean of a b s o r p t i o n s ) as compared to a standard d e v i a t i o n of 558 (35% of the mean of a b s o r p t i o n s ) . T h i s equation r e p r e s e n t s the h i g h e s t R 2 and lowest standard e r r o r without the i n c l u s i o n of dummy v a r i a b l e s f o r government programs. Since the p r e c i s e impacts of these programs c o u l d not be determined, these v a r i a b l e s were not i n c l u d e d i n the f i n a l a n a l y s i s . I t may be p o s s i b l e to improve these r e s u l t s by a d j u s t i n g the l a g s t r u c t u r e of the i n d i v i d u a l v a r i a b l e s . However, i t i s assumed that consumer response to changes i n economic ' c o n d i t i o n s w i l l be w i t h i n the q u a r t e r . F u r t h e r , to ad j u s t with d i f f e r e n t l a g s f o r each v a r i a b l e , without a p r i o r i reasons, may provide a b e t t e r f i t but does not comply with the model e x p e c t a t i o n s or make i n t u i t i v e sense. I t i s l o g i c a l to expect that the d e c i s i o n to form a household or rent a new housing u n i t w i l l be based on the c u r r e n t s t a t e of a l l v a r i a b l e s , not the s t a t e of some v a r i a b l e s f o r pr e v i o u s p e r i o d s i n an ad hoc arrangement. I t i s not d i s t u r b i n g that some v a r i a b l e s have the wrong s i g n , or are not s i g n i f i c a n t , i n l i g h t of the pr e v i o u s d i s c u s s i o n on m u l t i c o l l i n e a r i t y and data t r e n d s . The 87 i n s i g n i f i c a n c e o f m i g r a t i o n was a n t i c i p a t e d due t o t h e n a t u r e o f t h e v a r i a b l e ; f a m i l y a l l o w a n c e t r a n s f e r s f o r B r i t i s h C o l u m b i a i g n o r e i n t r a - p r o v i n c i a l m i g r a t i o n and h o u s e h o l d s w i t h o u t c h i l d r e n . New r e n t a l h o u s e h o l d s f r o m d e m o g r a p h i c c h a n g e h a s t h e wrong s i g n a n d i s n o t v e r y s i g n i f i c a n t . I n e s t i m a t i n g t h i s v a r i a b l e t h e u n r e a l i s t i c a s s u m p t i o n o f a c o n s t a n t r a t e o f g r o w t h b e tween c e n s u s y e a r s was made. C o n s e q u e n t l y , t h e number o f new r e n t a l h o u s e h o l d s was i n c r e a s i n g o v e r t h e t i m e p e r i o d a n d may be a c t i n g a s a t i m e v a r i a b l e , n o t m e a s u r i n g d e m o g r a p h i c c h a n g e . A l s o , i f d e m o g r a p h i c demand i n f l u e n c e s t h e l o n g r u n c y c l e , t h i s v a r i a b l e w o u l d n o t be e x p e c t e d t o be a s i m p o r t a n t f o r t h e s h o r t c y c l e . I n c r e a s e s i n r e a l r e n t s a r e e x p e c t e d t o r e d u c e t h e r a t e o f h o u s e h o l d f o r m a t i o n a n d s u b s e q u e n t l y t h e a b s o r p t i o n o f new r e n t a l u n i t s . The p o s i t i v e c o e f f i c i e n t i s i n i t i a l l y d i s t u r b i n g , s u g g e s t i n g e i t h e r t h a t t h e m o d e l i s n o t f u l l y s p e c i f i e d , o r t h a t o t h e r i n f l u e n c e s a r e b e i n g e x p l a i n e d t h r o u g h t h i s v a r i a b l e . A p o s s i b l e a r g ument t o s u p p o r t t h e p o s i t i v e c o e f f i c e n t i s t h a t i f r e a l o w n e r s h i p c o s t s h a v e d e c r e a s e d more t h a n r e a l r e n t s , t h e demand f o r o w n e r s h i p u n i t s w i l l h a v e i n c r e a s e d a t t h e e x p e n s e o f t h e demand f o r r e n t a l u n i t s . T h e r e f o r e t h e demand f o r r e n t a l u n i t s w o u l d h a v e d e c r e a s e d d e s p i t e d e c l i n i n g r e a l r e n t s . The p r o b l e m s o f m u l t i c o l l i n e a r i t y a n d t i m e t r e n d s a r e q u i t e p r e v e l a n t f o r t h e r e n t v a r i a b l e , p o s s i b l y e x p l a i n i n g t h e d i f f i c u l t i e s i n e s t i m a t i o n . A dummy f o r r e n t c o n t r o l s d i d n o t c o r r e c t t h e s i g n o r i m p r o v e t h e model s p e c i f i c a t i o n ( s e e e q u a t i o n 5, T a b l e 6.3). A l t e r n a t e f o r m s i n c l u d i n g . m o r t g a g e 88 r a t e s o r a d d i n g r e a l i n c o m e s a l s o d i d n o t c o r r e c t t h e p r o b l e m . T h e r e f o r e , d e s p i t e d i f f i c u l t i e s w i t h t h i s v a r i a b l e , i t h a s been l e f t i n t h e f i n a l r e s u l t s . S i n c e t h e unemployment r a t e was o n l y a v a i l a b l e f r o m 1966, a dummy v a r i a b l e was g e n e r a t e d t o c o m p e n s a t e f o r t h e m i s s i n g d a t a . 2 1 To d e t e r m i n e t h e f u l l i m p a c t o f unemployment a nd t h i s dummy v a r i a b l e , an e q u a t i o n was e s t i m a t e d u s i n g o n l y d a t a f o r 1966 t o 1980, where t h e r e was no m i s s i n g d a t a ( s e e e q u a t i o n 6, T a b l e 6 . 3 ) . A l t h o u g h t h e dummy v a r i a b l e i s s i g n i f i c a n t , i t d o e s n o t a l t e r t h e s i z e a n d m a g n i t u d e o f t h e o t h e r c o e f f i c i e n t s s u g g e s t i n g i t i s more a t i m e v a r i a b l e t h a n e x p l a i n i n g t h e i m p a c t o f t h e m i s s i n g unemployment d a t a . I t i s i m p o r t a n t t o n o t e t h a t t h e Home A c q u i s i t i o n P r o g r a m was s t a r t e d i n 1966, c o i n c i d i n g w i t h t h e m i s s i n g unemployment d a t a . I t i s n o t u n r e a s o n a b l e t o e x p e c t t h e dummy v a r i a b l e t o be i n c l u d i n g t h i s i m p a c t . H owever, i f t h i s were t r u e , t h e e x p e c t e d s i g n w o u l d be p o s i t i v e ; e n c o u r a g i n g home o w n e r s h i p w i l l . r e d u c e a p a r t m e n t d e m a n d . 2 2 From an e x a m i n a t i o n o f t h e a b s o r p t i o n d a t a i t i s o b v i o u s t h a t t h e p e r i o d o f 1963 t o 1965 had l o w e r a b s o r p t i o n s , b u t t h i s may be p a r t o f a c y c l e a n d n o t e x p l a i n e d w i t h i n t h e e c o n o m i c v a r i a b l e s . W i t h t h e e x i s t i n g d a t a , t h i s c a n n o t be t e s t e d f u r t h e r . The s t o c k v a r i a b l e was e s t i m a t e d a s t h e number o f r e n t a l h o u s e h o l d s m u l t i p l i e d by t h e o c c u p a n c y r a t e . C o n s e q u e n t l y , t h e v a c a n c y r a t e a n d s t o c k v a r i a b l e a r e h i g h l y c o r r e l a t e d . They a r e b o t h e n t e r e d i n t h e i n i t i a l e q u a t i o n , b u t v a c a n c i e s a r e removed f o r t h e r e m a i n i n g e s t i m a t i o n s . F i n a l l y , i n v e n t o r i e s r e p r e s e n t t h e c o n s t r a i n t f o r t h e 89 number of u n i t s absorbed. That i s , the number of u n i t s that can be rented i s l i m i t e d to those c u r r e n t l y a v a i l a b l e p l u s any completed d u r i n g the q u a r t e r . The number of u n i t s a v a i l a b l e i n i n v e n t o r y at the beginning of the p e r i o d i s entered to c o n t r o l f o r t h i s c o n s t r a i n t . The f i n a l e s t i m a t i o n f o r a b s o r p t i o n s which was used to c a l c u l a t e p r e d i c t e d a b s o r p t i o n s f o r the s t a r t s equation (equation 2, Table 6.3), c l e a r l y s u f f e r s data inadequancies and s p e c i f i c a t i o n p r o b l e m s . 2 3 However, given that the c o e f f i c i e n t s may be measuring more than the economic impacts and the poor aggregate data a v a i l a b l e , the r e s u l t s are not s u r p r i s i n g , or a l a r m i n g . The emphasis of t h i s paper i s not on the demand aspe c t s of m u l t i f a m i l y housing. T h e r e f o r e , r a t h e r than dwell on the inadequacies of t h i s e s t i m a t i o n , i t i s p r e f e r a b l e to move to the f i n a l r e s u l t s of the s t a r t s e q u a t i o n . 6.2.2 S t a r t s The i n t e r p r e t a t i o n of the s p e c i f i c r e s u l t s of the m u l t i f a m i l y s t a r t s equation i s more c r i t i c a l than the f i n a l a b s o r p t i o n equation. F o r t u n a t e l y , the e s t i m a t i o n does not s u f f e r the same problems with data inadequacies and m u l t i c o l l i n e a r i t y . A n a l y s i s of these r e s u l t s w i l l focus on the o v e r a l l model, whether the s i g n s and magnitudes of the c o e f f i c i e n t s are s i g n i f i c a n t and c o n s i s t e n t with the t h e o r e t i c a l e x p e c t a t i o n s and the p o s s i b i l i t y of a s t r u c t u r a l change f o r pre and post 1970. 2 4 T h e r e f o r e , the f u l l study p e r i o d has been used to determine the model s t r u c t u r e (1963-1980) and complete the 9 0 s e c o n d s t e p o f t h e a n a l y s i s . S i m i l a r e q u a t i o n s were t h e n e s t i m a t e d f o r 1963 t o 1970 a n d f o r 1971 t o 1980 t o d e t e r m i n e any c h a n g e s i n t h e m o d e l s t r u c t u r e . The s t a r t s e q u a t i o n was i n i t i a l l y e s t i m a t e d u s i n g a l l o f t h e v a r i a b l e s o u t l i n e d i n T a b l e 6.2, e x c e p t f o r t h e dummy v a r i a b l e s f o r g o v e r n m e n t p r o g r a m s ( e q u a t i o n 1, T a b l e 6 . 4 ) . The s t r u c t u r e o f t h e model assumes t h a t p r o d u c t i o n w i l l be d e p e n d e n t upon t h e p r e v i o u s p e r i o d V s l e v e l o f p r o d u c t i o n , c u r r e n t i n v e n t o r i e s a n d e x p e c t e d demand. I t i s n o t p o s s i b l e t o d e t e r m i n e d e s i r e d i n v e n t o r i e s , t h e r e f o r e a p r o f i t p r o x y and t h e bank r a t e h a v e been e n t e r e d i n t o t h e e q u a t i o n d i r e c t l y . Q u a r t e r l y dummies a r e u s e d t o remove any s e a s o n a l i t y i n t h e s e r i e s . G i v e n t h i s s t r u c t u r e , t h e o v e r a l l model d o e s n o t a p p e a r v e r y s a t i s f a c t o r y w i t h an a d j u s t e d R 2 o f o n l y 0.268 and a s t a n d a r d e r r o r o f 38 p e r c e n t o f t h e mean o f s t a r t s . P r e v i o u s d i s c u s s i o n c o n s i d e r e d w h e t h e r b o t h u n i t s u n d e r c o n s t r u c t i o n a n d i n v e n t o r y s h o u l d be i n c l u d e d i n t h e f i n a l e s t i m a t i o n . I t may be a r g u e d t h a t s t a r t s s h o u l d be r e s p o n d i n g t o b o t h , h o w e v e r , t h e r e i s some d i f f i c u l t y i n t h e d a t a f o r u n i t s u n d e r c o n s t r u c t i o n a s i t i s u s e d a s a c o r r e c t i o n f a c t o r i n t h e s t o c k v a r i a b l e s . U n i t s u n d e r c o n s t r u c t i o n a r e e n t e r e d i n t o t h e f i r s t e q u a t i o n , b u t s i n c e t h i s v a r i a b l e i s i n s i g n i f i c a n t , i t h a s been o m i t t e d f r o m f u r t h e r r u n s . The o m i s s i o n o f u n i t s u n d e r c o n s t r u c t i o n i n c r e a s e s t h e a d j u s t e d R 2 t o 0.278; s t i l l n o t v e r y s a t i s f a c t o r y . Some i n t e r e s t r a t e a n d a p r o f i t a b i l i t y m e a s u r e a r e g i v e n i n t h e f u n c t i o n e q u a t i o n f o r d e s i r e d i n v e n t o r i e s a n d t h e r e f o r e Table 6.4 Regression Results - Multi Family Housing Starts 1963-1980 CONSTANT VMFST1 ABSPRED VMFINV1 VMFUC1 PROFIT BKRAT 02 03 04 DUM MURB R« SE/DW 1 -992 0 .277 0 .625 -0 . 180 -0. 020 1 1 .417 33. 836 170.42 287.61 394.51 .362 646.87 (2 .026) (2 .314) (0 .951 ) (0. 411) (0 .960) (0. 633) (0.746) ( 1 .254) (1.751 ) .268 2.023 2 . -1137 0 .252 0 .587 -0 . 169 12 .552 37. 439 167.92 292.44 400.65 . 361 642.54 (2 .070) (2 .329) (0. .907) (1 .092) (0. 714) (0.740) ( 1 .286) ( 1 .795) .278 1 .999 3 185 0 .258 0 .691 -0 .277 161.66 278.89 407.39 .347 638.83 (2 . 157) < 3 .081 ) (1. .750) (0.719) ( 1 .235) (1.846) .286 2.004 4 341 0 223 0 .775 -0. 295 • .310 642 . 10 (1. 945) (3. .545) (1 865) .297 1 .937 5 238 0. 235 0 676 -0. 336 271.57 353.65 450.13 354 . 19 .429 602.15 (2. 079) (3. 197) (2. 233) ( 1 .263) (1.650) (2.158) (3.006) .366 1 .991 6 223 0. 235 0. 674 -0. 340 271.76 355.11 451.62 354.63 21 .49 .429 606.94 (2. 065) (3. , 159) (2. 182) ( 1 .254) (1.640) (2.143) (2.984) (0.010) .356 1 .993 Notes: (1) t - s t a t l s t i c s in parenthesis (2) a '1' a f t e r the variable name Indicates that the variable is lagged one period (3) R' values reported are: f i r s t the unadjusted R', and second the adjusted R1 (4) SE/DW denotes the standard error and Durbln-Watson s t a t i s t i c 92 enter the e s t i m a t i o n . However, the i n t e r e s t r a t e (bank r a t e ) i s not s i g n i f i c a n t and has the wrong s i g n . Smith (1979) found m u l t i f a m i l y housing to be i n s e n s i t i v e to c r e d i t a v a i l a b l i l i t y , but s e n s i t i v e to c r e d i t c o s t s . Other s t u d i e s (Rosen, J a f f e e and Rosen) have used i n t e r e s t r a t e s and found them s i g n i f i c a n t with v a r y i n g c o e f f i c i e n t s . I t i s p o s s i b l e that the nature of m u l t i f a m i l y c o n s t r u c t i o n i s i n f l u e n c i n g t h i s v a r i a b l e . C o n s t r u c t i o n loans are n e g o t i a t e d before the s t a r t and t h e r e f o r e i t may be more c o r r e c t to l a g t h i s v a r i a b l e more than one p e r i o d . Other c r e d i t c o n d i t i o n s such as the term, a m o r t i z a t i o n p e r i o d , any o r i g i n a t i o n or lender fees and the non-standard design of these loans may mean that a c t u a l c r e d i t c o s t s are not f u l l y r e presented by the nominal i n t e r e s t r a t e . P r o f i t does have the c o r r e c t s i g n but i s m a r g i n a l l y s i g n i f i c a n t . I t should not be dis c o u n t e d merely on the ba s i s of i t s s i g n i f i c a n c e . C l e a r l y , p r o f i t a b i l i t y w i l l i n f l u e n c e the investment d e c i s i o n , however the proxy may be inadequate to a c c u r a t e l y r e f l e c t market c o n d i t i o n s . 2 5 Due to the p o s s i b l e d i f f i c u l t i e s with the p r o f i t proxy and i n t e r e s t r a t e s , the next r e g r e s s i o n excluded these two v a r i a b l e s , improving the adj u s t e d R 2 to 0.286 (equation 3, Table 6.4). T h i s provided the best o v e r a l l model without any adjustments f o r government programs. F i n a l e s t i m a t i o n s excluded the q u a r t e r l y dummies to co n f i r m the s e a s o n a l i t y e x p e c t a t i o n and then i n c l u d e d a dummy f o r MURBs and the unusual data i n 1977 to 1 978 . 2 6 L i t t l e i s gained with the MURB dummy, or other dummies which were t e s t e d f o r other government programs. The impacts of 9 3 t h e s e p r o g r a m s a r e u n d o u b t e d l y t o o c o m p l e x t o be c a p t u r e d w i t h a z e r o / o n e v a r i a b l e , b u t t h e r e i s i n s u f f i c i e n t k n o w l e d g e on m a r k e t r e s p o n s e s t o s t r u c t u r e a more s o p h i s t i c a t e d v a r i a b l e . E q u a t i o n s 3 and 5 ( T a b l e 6.4) p r o v i d e d t h e b e s t o v e r a l l r e s u l t s . The f o l l o w i n g d i s c u s s i o n on t h e s p e c i f i c c o e f f i c i e n t s w i l l k ey on t h e s e r e s u l t s . L a g g e d s t a r t s a r e e x p e c t e d t o h a v e a p o s i t i v e s i g n b a s e d on t h e a d j u s t m e n t p r o c e s s o f t h e i n v e n t o r y m o d e l . The c o e f f i c i e n t f o r t h i s v a r i a b l e i n d i c a t e s t h e s p e e d o f a d j u s t m e n t o f s t a r t s t o t h e d e s i r e d l e v e l . F o r t h e c o m p l e t e e s t i m a t i o n p e r i o d , t h i s c o e f f i c i e n t o f 0.258 ( E q u a t i o n 3) o r 0.235 ( E q u a t i o n 5 ) . T h e r e f o r e , t h e mean l a g o f t h e a d j u s t m e n t p r o c e s s i s a p p r o x i m a t e l y one t h i r d . 2 7 T h a t i s , a d j u s t m e n t w i l l o c c u r w i t h i n one t h i r d o f a q u a r t e r , w h i c h s u g g e s t s an a l m o s t i n s t a n t a n e o u s a d j u s t m e n t . A b s o r p t i o n s r e p r e s e n t t h e e x p e c t e d demand, w h i c h , t o m a i n t a i n a c o n s t a n t l e v e l o f i n v e n t o r y w i l l h a v e c l o s e t o a one- t o - o n e r e l a t i o n s h i p w i t h s t a r t s . Some r e s p o n s e l a g i s e x p e c t e d d e p e n d i n g on o t h e r m a r k e t c o n d i t i o n s . A l s o , t h e l u m p i n e s s o f m u l t i f a m i l y u n i t s may a f f e c t t h e r e s p o n s e t o demand; i t i s o b v i o u s l y n o t p o s s i b l e t o b u i l d one m u l t i f a m i l y u n i t . D e p e n d i n g on t h e s i z e o f p l a n n n e d p r o j e c t s , t h e r e s p o n s e r a t e o f m a r k e t p a r t i c i p a n t s w i l l v a r y . T h e r e f o r e , a c o e f f i c i e n t a r o u n d 0.6 i s r e a s o n a b l e and w i t h i n t h e t h e o r e t i c a l e x p e c t a t i o n . The p r e m i s e o f t h e t h e o r e t i c a l m o d e l i s t h a t t h e r e i s some d e s i r e d i n v e n t o r y l e v e l t o be m a i n t a i n e d , d e p e n d i n g on t h e c o s t of h o l d i n g v a c a n t u n i t s . As t h e a c t u a l number o f u n i t s i n 94 i n v e n t o r y i n c r e a s e s , s t a r t s s h o u l d d e c l i n e . C o n v e r s e l y , a r e d u c t i o n i n i n v e n t o r y s h o u l d g e n e r a t e an i n c r e a s e i n s t a r t s t o r e p l e n i s h t h e s t o c k . I n v e n t o r i e s do have t h e e x p e c t e d n e g a t i v e c o e f f i c i e n t . A s e c o n d c o n s i d e r a t i o n i s t h e s i z e o f t h e c o e f f i c i e n t a n d w h e t h e r i t make s e n s e w i t h i n t h e s t r u c t u r a l f r a m e w o r k o f t h e m o d e l . The c o e f f i c i e n t o f a p p r o x i m a t e l y -0.3 i n d i c a t e s t h a t e x p e c t e d s t a r t s w i l l be r e d u c e d by a b o u t 30 p e r c e n t o f t h e e x i s t i n g i n v e n t o r y . The r e g r e s s i o n o f c o m p l e t i o n s w i t h l a g g e d s t a r t s i n d i c a t e d t h a t t h e e x p e c t e d c o n s t r u c t i o n t i m e f r o m s t a r t t o c o m p l e t i o n was b e t w e e n 6 months t o 1 y e a r . I t h a s a l s o b een s u g g e s t e d t h a t t h e r e s p o n s e s h o u l d be l e s s t h a n one t o a c c o m o d a t e an a d j u s t m e n t l a g b e t w e e n c h a n g e s i n i n v e n t o r y a n d s t a r t s . A l t h o u g h t h i s v a r i a b l e i s o n l y m a r g i n a l l y s i g n i f i c a n t f o r some o f t h e e q u a t i o n s , t h e s i z e o f t h e c o e f f i c i e n t i s c o n s i s t e n t w i t h e x p e c t a t i o n s . F u r t h e r , i t s s i z e d o e s n o t c h a n g e d r a s t i c a l l y when t h e s a m p l e i s s p l i t f o r t h e p r e and p o s t 1970 a n a l y s i s . F i n a l l y , t h e q u a r t e r l y dummies i n d i c a t e t h a t t h e r e i s some s e a s o n a l i t y w i t h t h e f i r s t q u a r t e r b e i n g t h e l o w e s t . A l t h o u g h t h e s e c o e f f i c i e n t s a r e n o t v e r y s i g n i f i c a n t i n d i v i d u a l l y , t h e y do i m p r o v e t h e o v e r a l l m o d e l a n d have been m a i n t a i n e d i n t h e e s t i m a t i o n . An e x a m i n a t i o n o f t h e r e s i d u a l s f o r e q u a t i o n s 3 a n d 5 ( F i g u r e s 6.1 a n d 6.2) i n d i c a t e some c y c l i n g w h i c h i s n o t e x p l a i n e d by t h e i n d e p e n d e n t v a r i a b l e s . The l i t e r a t u r e s u g g e s t s t h a t h o u s i n g c y c l e s may be a n t i - c y c l i c a l t o t h e g e n e r a l b u s i n e s s c y c l e . The r e a l C a n a d i a n g r o s s n a t i o n a l p r o d u c t was u s e d a s a F I G U R E 6 . 1 - R E S I D U A L A N A L Y S I S FOR E Q U A T I O N 3 - 3 . 0 0.0 3.0 S T A R T S P R E D I C T E D R E S I D U A L Y E A R : QTR 0 : : 0 S T A R T S 1 9 6 3 : 1 9 7 1 . 2 V . . 8 2 0 . 1 1 0 4 . 0 5 4 1 - 2 8 4 . 0 5 4 1 3 1 2 3 1 . 1 2 5 0 . 0 2 7 6 - 1 9 . 0 2 7 6 4 . ^ » 2 0 4 5 . 1 5 2 1 . 5 0 2 2 5 2 3 . 4 9 7 8 1 9 6 4 : 1 . <T 1 5 9 2 . 1 3 2 8 . 2 0 8 9 2 6 3 . 7 9 1 1 2 1 9 8 4 . 1 3 9 6 . 1 9 6 3 5 8 7 . 8 0 3 7 3 . ̂ _____I^>« 2 9 2 8 . 1 6 4 4 . 4 9 2 3 1 2 8 3 . 5 0 7 7 4 — " - 1 9 9 2 . 2 0 4 4 . 5 7 4 0 - 5 2 . 5 7 4 0 1 9 6 5 : 1 1 1 6 4 . 1 4 9 8 . 7 9 2 2 - 3 3 4 . 7 9 2 2 2 • ' 3 1 0 8 . 1 5 1 9 . 8 6 4 5 1 5 8 8 . 1 3 5 5 3 1 8 8 4 . 2 0 6 6 . 3 7 0 4 - 1 8 2 . 3 7 0 4 4 • 1 4 3 0 . 1 9 4 8 . 9 6 8 9 - 5 1 8 . 9 6 8 9 1 9 6 6 : 1 J* 1 2 2 0 . 1 6 1 0 . 2 2 5 4 - 3 9 0 . 2 2 5 4 2 <T 9 2 0 . 1 7 8 1 . 1 5 9 2 - 8 6 1 . 1 5 9 2 3 J> 1 3 4 9 . 1 8 9 3 . 7 1 2 7 - 5 4 4 . 7 1 2 7 4 <CT . . 1 1 8 4 . 2 0 8 2 . 6 7 3 6 - 8 9 8 . 6 7 3 6 1 9 6 7 : 1 . 1 1 2 8 . 1 5 1 5 . 4 0 6 4 - 3 8 7 . 4 0 6 4 2 1 6 7 8 . 1 6 7 6 . 7 4 0 7 1 . 2 5 9 3 3 ^^ - 1 -_Z>« 2 7 5 6 . 2 0 9 0 . 0 6 9 0 6 6 5 . 9 3 1 0 4 «<C^T^ 1 7 9 8 . 2 4 1 8 . 7 9 7 7 - 6 2 0 . 7 9 7 7 1 9 6 8 : 1 " " ^ ^ . ^ 1 9 3 2 . 1 6 5 8 . 1 3 7 2 2 7 3 . 8 6 2 8 2 2 7 3 5 . 1 9 4 0 . 7 2 8 8 7 9 4 . 2 7 1 2 3 « < ^ _ 2 0 5 1 . 2 3 8 2 . 5 0 0 8 - 3 3 1 . 5 O 0 8 4 . 3 0 0 3 . 2 3 8 7 . 8 5 3 4 6 1 5 . 1 4 6 6 1 9 6 9 : 1 N 3 0 3 1 . 2 1 9 5 . 6 9 5 5 8 3 5 . 3 0 4 5 2 . > . 3 4 4 5 . 2 4 3 8 . 9 7 7 1 1 0 0 6 . 0 2 2 9 3 . • 3 6 2 7 . 2 7 5 7 . 5 6 8 5 8 6 9 . 4 3 1 5 4 * • . 1 8 4 2 . 2 9 6 9 . 3 6 0 7 - 1 1 2 7 . 3 6 0 7 1 9 7 0 : 1 . 2 0 2 0 . 1 9 5 9 . 7 9 1 3 6 0 . 2 0 8 7 2 . 6 3 4 . 2 0 2 2 . 0 9 2 9 - 1 3 8 8 . 0 9 2 9 3 1 8 9 9 . 1 9 8 3 . 6 1 7 1 - 8 4 . 6 1 7 1 4 . 3 2 1 3 . 2 4 8 4 . 7 3 9 1 7 2 8 . 2 6 0 9 1 9 7 1 : 1 2 2 6 1 . 2 0 5 4 . 8 8 4 8 2 0 6 . 1 1 5 2 2 <T . . 1 8 7 5 . 2 0 6 2 . 9 8 6 4 - 1 8 7 . 9 8 6 4 3 V. 2 0 9 9 . 2 2 6 8 . 9 2 0 0 - 1 6 9 . 9 2 0 0 4 2> 2 5 8 7 . 2 4 0 8 . 8 0 8 6 1 7 8 . 1 9 1 4 1 9 7 2 : 1 • 1 2 8 8 . 1 8 3 9 . 0 2 4 0 - 5 5 1 . 0 2 4 0 2 ^ t . • 1 4 9 3 . 1 6 3 9 . 7 0 9 7 - 1 4 6 . 7 0 9 7 3 1 7 7 9 . 1 8 9 8 . 1 3 5 3 - 1 1 9 . 1 3 5 3 4 ^^_J> 2 3 3 6 . 2 0 3 5 . 1 0 2 1 3 0 0 . 8 9 7 9 1 9 7 3 : 1 -<d^. 9 5 9 . 1 6 8 8 . 8 7 9 5 - 7 2 9 . 8 7 9 5 2 1 6 8 6 . 1 5 2 6 . 3 4 2 4 1 5 9 . 6 5 7 6 3 1 6 7 4 . 1 8 9 1 . 2 3 7 8 - 2 1 7 . 2 3 7 8 4 2 9 6 3 . 2 0 2 0 . 9 3 2 7 9 4 2 . 0 6 7 3 1 9 7 4 : 1 1 1 2 8 . 1 8 0 2 . 7 3 6 9 - 6 7 4 . 7 3 6 9 2 2 1 8 1 . 1 4 3 7 . 0 7 5 3 7 4 3 . 9 2 4 7 3 T " ! 1 5 2 5 . 1 7 5 3 . 6 5 4 6 - 2 2 8 . 6 5 4 6 4 > . 1 5 1 5 . 1 6 7 1 . 7 4 2 8 - 1 5 6 . 7 4 2 8 1 9 7 5 : 1 \ . 7 0 0 . 1 0 9 3 . 8 7 1 1 - 3 9 3 . 8 7 1 1 2 8 5 5 . 1 1 3 4 . 3 8 4 3 - 2 7 9 . 3 8 4 3 3 7 ^ > » 1 7 2 7 . 1 2 7 0 . 0 1 4 8 4 5 6 . 9 8 5 2 4 <7 1 5 8 7 . 1 7 2 5 . 7 1 0 2 - 1 3 8 . 7 1 0 2 1 9 7 6 : 1 < . 1 0 1 5 . 1 1 5 0 . 5 1 7 6 - 1 3 5 . 5 1 7 6 2 _ 1 5 0 7 . 1 2 1 5 . 5 9 0 7 2 9 1 . 4 0 9 3 3 1 2 1 0 . % 1 4 7 3 . 4 3 4 1 - 2 6 3 . 4 3 4 1 4 7ĵ >» 2 3 7 2 . 1 5 8 9 . 4 4 8 6 7 8 2 . 5 5 1 4 1 9 7 7 : 1 *<CZ 1 4 3 5 . 1 4 2 9 . 7 4 7 7 5 . 2 5 2 3 2 .J^>* 1 9 0 3 . 1 4 3 4 . 7 5 2 0 4 6 8 . 2 4 8 0 3 1 6 1 2 . 1 7 8 7 . 6 0 6 9 - 1 7 5 . 6 0 6 9 4 T^-*-^^ 2 1 3 2 . 1 8 4 5 . 1 2 0 6 2 8 6 . 8 7 9 4 1 9 7 8 : 1 2 2 0 6 . 1 3 4 6 . 2 6 8 3 8 5 9 . 7 3 1 7 2 * = r — " ' 2 9 0 . 1 6 2 9 . 8 7 0 5 - 1 3 3 9 . 8 7 0 5 3 3 7 3 - 1 2 2 6 . 7 9 1 0 - 8 5 3 . 7 9 1 0 4 ^ * - ^ _ . 6 8 6 . 1 2 2 9 . 8 6 0 3 - 5 4 3 . 8 6 0 3 1 9 7 9 : 1 J^>> 1 1 1 5 . 8 0 6 . 3 6 4 9 3 0 8 . 6 3 5 1 2 " ^ " ^ 6 3 2 . 1 1 6 6 . 5 1 1 8 - 5 3 4 . 5 1 1 8 3 J> . 1 0 1 3 . 1 2 7 2 . 7 1 3 7 - 2 5 9 . 7 1 3 7 4 7 6 5 . 1 4 5 2 . 7 9 7 9 . - 6 8 7 . 7 9 7 9 1 9 8 0 : 1 J^Z^* 1 5 7 4 . 7 8 9 . 4 4 8 6 7 8 4 . 5 5 1 4 2 *"=CT""! 6 2 6 . 1 2 4 4 . 9 6 3 3 - 6 1 8 . 9 6 3 3 3 T % 1 3 3 4 . 1 1 6 0 . 1 3 3 6 1 7 3 . 8 6 6 4 4 . ^ 1 9 0 1 . 1 5 1 3 . 0 0 6 7 3 8 7 . 9 9 3 3 Y E A R : QTR 0 : : 0 - 3 . 0 0 . 0 3 . 0 FIGURE 6.2 - RESIDUAL ANALYSIS FOR EQUATION 5 -3.0 0.0 3:0 STARTS PREDICTED RESIDUAL YEAR: QTR 0: :0 STARTS 1963:1 . 9 7 1 . -0.100OE+07 -0.1000E+07 2 . \ . 820. 1216.5122 - 3 9 6 . 5 1 2 2 3 1231. 1318.0302 - 8 7 . 0 3 0 2 4 2045. 1547.1288 497.8712 1964:1 . / 1592. 1281.8199 310.1801 2 - . V 1984. 1476.6967 507.3033 3 2928. 1680.3339 1247.6661 4 f" 1992. 2017.4753 - 25 .4753 1965:1 1164. 1378.2870 - 2 1 4 . 2 8 7 0 2 . 3108. 1511.7118 1596.2882 3 > r 1884. 2038.5488 - 1 5 4 . 5 4 8 8 4 it; . 1430. 1893.9440 - 4 6 3 . 9 4 4 0 196S:1 1220. 1557.2904 - 3 3 7 . 2 9 0 4 2 < ^ 920. 1847.9164 - 9 2 7 . 9 1 6 4 3 j> 1349. 1924.2876 - 5 7 5 . 2 8 7 6 4 <C . 1 1 8 4 . 2082.4273 - 8 9 8 . 4 2 7 3 1967:1 . . 1 1 2 8 . 1485.2835 - 3 5 7 . 2 8 3 5 2 1678. 1769.5482 - 9 1 . 5 4 8 2 3 ^ ^ j . ^ s - 2756. 2125.7629 630.2371 4 *<^r_ 1798. 2399.2097 - 6 0 1 . 2 0 9 7 1968:1 r—V. 1932. 1623.8722 308.1278 2 ^ ^ ~ ~ > > 2735. 20O6.0127 728.9873 3 «<Ĉ T 2051. 2403.5798 - 3 5 2 . 5 7 9 8 4 3003. 2393.9473 609 .0527 1969:1 ^ 3031. 2125 .6450 9 0 5 . 3 5 5 0 2 / 3445. 2479.0508 965 .9492 3 — * 3627. 2753.4809 873.5191 4 ——_____~7 1842. 2918.1153 - 1 0 7 6 . 1 1 5 3 1970:1 — 2020. 1898.1850 121.8150 2 *<^^rl 6 3 4 - 2051.3606 - 1 4 1 7 . 3 6 0 6 3 - " " S ^ ^ ^ 1899. 2025.8939 - 1 2 6 . 8 9 3 9 4 . J > * 3213. 2443.7191 769 .2809 1971:1 2261. 1988.1171 272 .8829 2 \ \ 1875. 2105.5579 - 2 3 0 . 5 5 7 9 3 V. 2099. 2261 .5210 - 1 6 2 . 5 2 1 0 4 2587. 2358.0681 228.9319 1972:1 «<r". 1288. 1767.5280 - 4 7 9 . 5 2 8 0 2 \ . 1493. 1723.2381 -230 .2381 3 V. 1779. 1928.4141 -149 .4141 4 ^ ^ ^ S * 2336. 2037.3425 298.6575 1973:1 *<CT. 959 . 1638.6861 -679 .6861 2 ^ > 1686. 1623.3503 62 .6497 3 1674. 1918.6161 -244 .6161 4 ' • 2963. 2023 .9507 939 .0493 1974:1 _ _ _ _ 1128. 1749.7756 - 6 2 1 . 7 7 5 6 2 J ] ] ^ > * 2181. 1533.9738 647 .0262 3 r"*T" . 1525. 1790.3828 - 2 6 5 . 3 8 2 8 4 V . 1 5 1 5 . 1671.6707 - 1 5 6 . 6 7 0 7 1975:1 f . 700. 1040.3700 - 3 4 0 . 3 7 0 0 2 855 . 1185.3028 - 3 3 0 . 3 0 2 8 3 \j^> 1727. 1254.8968 472.1032 4 if; 1587. 1673.9795 - 8 6 . 9 7 9 5 1976:1 V 1015. 1043.7362 - 2 8 . 7 3 6 2 2 J> 1507. 1241.2898 265.7102 3 « < - ^ _ _ _ ^ 1210. 1461.4285 - 2 5 1 . 4 2 8 5 4 . 2372. 1531.3736 840 .6264 1977:1 1435. 1303.2487 131.7513 2 . ^ i * 1903. 1445.8177 457 .1823 3 *T 1612. 2077.4231 -465 .4231 4 V . 2132. 2444 .4816 - 3 1 2 . 4 8 1 6 1978:1 / . 2206. 2293.2257 - 8 7 . 2 2 5 7 2 \ . 290. 556 .5535 - 2 6 6 . 5 5 3 5 3 / . 373. 542.9858 - 1 6 9 . 9 8 5 8 4 "C. 686. 898.4314 - 2 1 2 . 4 3 1 4 1979:1 _ ^ > » 1115. 791.9354 323.0646 2 rT" 7 632. 1254.2208 - 6 2 2 . 2 2 0 8 3 J> 1013. 1320.4895 - 3 0 7 . 4 8 9 5 4 765. 1480.6049 - 7 1 5 . 6 0 4 9 1980:1 ~ ^ - ~ ^ = a m 1574. 800.9942 773.0058 2 *<r"~"7 626. 1343.8859 - 7 1 7 . 8 8 5 9 3 ^"""""T-'k 1334. 1244.9243 89 .0757 4 . ^ 1901. 1535.1301 365.8699 YEAR : QTR 0 : :0 97 proxy to t e s t t h i s p o s s i b i l i t y . I t d i d not improve the model or reduce the c y c l e i n the r e s i d u a l s . A second c o n s i d e r a t i o n i n the r e s i d u a l a n a l y s i s i s the r e d u c t i o n i n the s i z e of the e r r o r s a f t e r 1971. T h i s c o i n c i d e s with the e x p e c t a t i o n of a p o s s i b l e change in the market s t r u c t u r e f o r pre and post 1970. The r e s u l t s of t h i s a n a l y s i s confirms t h i s e x p e c t a t i o n . The estimated equations f o r 1963 to 1970 are presented i n Table 6.5. These r e s u l t s are much poorer than the r e s u l t s f o r the t o t a l time p e r i o d ; the a d j u s t e d R 2 f o r equation 3 i s reduced to 0.109 and the standard e r r o r i s i n c r e a s e d to 52 per cent of the mean of s t a r t s f o r t h i s p e r i o d . The c o e f f i c i e n t s f o r s t a r t s , p r e d i c t e d a b s o r p t i o n s and inventory have the same s i g n s , but the s i z e s and s i g n i f i c a n c e are very d i f f e r e n t . In the e s t i m a t i o n f o r the t o t a l p e r i o d , a b s o r p t i o n s were the most s i g n i f i c a n t v a r i a b l e . In the 1963-70 p e r i o d , lagged s t a r t s are most s i g n i f i c a n t . A l s o , the s i z e of the c o e f f i c i e n t s f o r the q u a r t e r l y dummies are q u i t e d i f f e r e n t , suggesting a s h i f t i n the s e a s o n a l i t y . The reasons f o r the poor f i t may be i n the e s t i m a t i o n , or the reduced number of o b s e r v a t i o n s (reducing the degrees of freedom). The p r e d i c t e d a b s o r p t i o n s i s based on data f o r the f u l l p e r i o d . Consequently, l a t e r p e r i o d s may b i a s t h i s v a r i a b l e , however, i t i s not expected that t h i s b i a s w i l l a f f e c t the r e s u l t s d r a s t i c a l l y . The e x p e c t a t i o n s of a change i n market s t r u c t u r e i s supported by the e s t i m a t i o n of the equations f o r 1971-1980 (see Table 6.6). The o v e r a l l model r e s u l t s are b e t t e r . The removal Table 6.5 Regression Results - Multi Family Housing Starts 1963-1970 CONSTANT VMFST1 ABSPRED VMFINV1 VMFUC1 PROFIT BKRAT 02 03 04 OUM MURB R' SE/DW 1 . 5074 0.435 -0.046 0. 308 -0. 135 -45.467 182.836 378.610 649.847 355.289 .346 795.81 ( 1 .366) (0.045) (0.491) (0. 892) (0.555) (O.734) (0.899) (1.358) (0.715) .066 1 .923 2 . 8920 0.252 ' -O.337 0. 127 -75.566 96.281 386.665 653.133 420.982 .321 792. 1 1 (1.040) (0.351) (0.214) (1.017) (0.422) (0.922) ( 1 .372) (0.861) .075 1 .845 3 327 0.388 0.471 -0.221 317.558 446.749 168.927 .287 777.20 (2.037) ( 1 .258) (0.580) (0.783) (1.097) (0.415) . 109 1 .899 4 632 0.366 -0.283 0.481 .247 752.98 (2.044) (0.780) ( 1 .329) . 163 1 .873 Notes: (1) t - s t a t l s t l c s In parenthesis (2) a '1' a f t e r the variable name Indicates that the'varIable Is lagged one period (3) R' values reported are: f i r s t the unadjusted R', and second the adjusted R1 (4) SE/DW denotes the standard error and Durbln-Watson s t a t i s t i c Table 6.6 Regression Results - Multi Family Housing Starts 1971-1980 CONSTANT VMFST1 ABSPRED VMFINV1 VMFUC1 PROFIT BKRAT 02 03 04 DUM MURB R' SE/DW 1 . -1674 -0 (0 . 106 .510) 1 (1 .242 .791 ) -0 (1 .285 .056) 0.061 (0.842) 10. (0. . 186 481 ) 75.898 (1.112) -197.679 (0.678) -193.874 (0.581) 245.538 (0.756) .452 .288 531.75 2 .040 2 . -1697 -0 (0 .031 . 164) 1 (1 .020 .598) -0. (0. .238 .905) 18 . (0. 422 986) 54.299 (0.862) -135.539 (0.483) -113.680 (0.357) 321 .369 ( 1 .034) .439 . 295 529.25 2 .034 3. 235 -d (0 .023 . 123) 1 (3 .087 .015) -0. (1. 334 .822) -164.833 (0.604) -128.356 (0.436) 345.354 ( 1 .244) .417 .311 523.03 2.036 4 . 20O -o. (0. 014 093) 1 (3 . 102 .471 ) -0. (1. 321 748) .313 .256 543.70 2.086 5. 308 -0. (0. 045 295) 1 (3 .034 .438) -0. (2. 405 628) 31.267 (0.134) 13.113 (0.053) 419.760 (1.806 ) 343.077 (3.923) .606 .520 436.45 2. 198 6 . 442 -0. (0. ,062 396) 1 (3 .006 .288) -0. (1. 341 917) 19.477 (0.083) -17.573 (0.069) 391 .851 ( 1 .651 ) 338.543 (3.833) -142.44 (0.742) .613 .513 439.73 2 . 183 Notes: (1) t-stat1st1cs in parenthesis (2) a '1' a f t e r the variable name indicates that the variable is lagged one period (3) R* values reported are: f i r s t the unadjusted R1, and second the adjusted R' (4) SE/DW denotes the standard error and Durbin-Watson s t a t i s t i c VO VO 100 o f t h e 1977-78 a b n o r m a l d a t a w i t h a dummy s i g n i f i c a n t l y i m p r o v e d t h e r e s u l t s w i t h an a d j u s t e d R 2 o f .52 and t h e s t a n d a r d e r r o r r e d u c e d t o 436 (29 p e r c e n t o f t h e mean o f s t a r t s ) . S e v e r a l o f t h e c o e f f i c i e n t s a r e q u i t e d i f f e r e n t f o r t h e two p e r i o d s . The n e g a t i v e a n d i n s i g n i f i c a n t c o e f f i c i e n t f o r l a g g e d s t a r t s f o r t h e 1971-80 p e r i o d may be i n t e r p r e d t e d a s z e r o , o r i m m e d i a t e a d j u s t m e n t . The c o e f f i c i e n t f o r p r e d i c t e d a b s o r p t i o n s i n c r e a s e d w h i c h may be i n p a r t due t o t h e l o w e r v a c a n c y r a t e s e x p e r i e n c e d d u r i n g t h e 1 9 7 0 ' s . W i t h f e w e r e x i s t i n g u n i t s a v a i l a b l e , t h e demand a n d a b s o r p t i o n f o r new u n i t s s h o u l d i n c r e a s e . The c o e f f i c i e n t f o r i n v e n t o r i e s i s r e l a t i v e l y s t a b l e , b u t more s i g n i f i c a n t . I f t h e mo d e l i s r e f l e c t i n g m a r k e t r e s p o n s e s , t h e s e c h a n g e s s u g g e s t t h a t t h e m a r k e t t h r o u g h o u t t h e 1970's was more r e s p o n s i v e t o demand a n d i n v e n t o r i e s , s u p p o r t i n g t h e i n v e n t o r y a d j u s t m e n t a p p r o a c h . The p o s s i b i l i t y o f a c h a n g e i n s e a s o n a l i t y i s a l s o s u p p o r t e d . The r a t i o o f t h e f o u r t h q u a r t e r dummy t o e i t h e r o f t h e o t h e r q u a r t e r s i s s u b s t a n t i a l l y l a r g e r t h a n f o r t h e r e s u l t s f o r e i t h e r t h e t o t a l p e r i o d , o r t h e 1963-70 p e r i o d . S m i t h ( 1 9 7 9 ) p r o p o s e d t h a t s t a r t s i n t h e f o u r t h q u a r t e r were i n c r e a s e d i n r e s p o n s e t o a n n u a l e x p e c t a t i o n s o f r e m o v a l o f t h e MURB b e n e f i t s . T h e s e r e s u l t s w o u l d seem t o s u p p o r t t h i s p r o p o s a l . O v e r a l l , t h e model p e r f o r m s b e t t e r f o r t h e p o s t 1970 p e r i o d , b u t , t h e r e s u l t s a r e n o t a s go o d a s t h o s e s t u d i e s r e v i e w e d . 2 8 The s i g n i f i c a n c e o f t h e i n v e n t o r y , a b s o r p t i o n s a n d s t a r t s v a r i a b l e s i s e n c o u r a g i n g a n d s u p p o r t t h e p r o p o s e d t h e o r e t i c a l s t r u c t u r e o f an i n v e n t o r y a d j u s t m e n t m o d e l . 101 The proposed t h e o r e t i c a l model suggests that i n v e n t o r y l e v e l s a ct as a b u f f e r between the supply and demand f o r m u l t i f a m i l y housing u n i t s . The t r a d i t i o n a l measure has been vacancy r a t e s with the argument that d u r i n g p e r i o d s of low vacancy r a t e s , investment and subsequently s t a r t s f o r m u l t i f a m i l y ( r e n t a l ) housing'should i n c r e a s e . As a t e s t of the v a l i d i t y of the c l a i m that vacancy r a t e s are not a s u f f i c i e n t i n d i c a t o r of demand and supply m o t i v a t i o n , four a d d i t i o n a l equations are re p o r t e d . These are the best o v e r a l l models from the above a n a l y s i s , with vacancy r a t e s f o r the beginning of the quarter added with p r e d i c t e d a b s o r p t i o n s s t i l l i n the e s t i m a t i o n and with p r e d i c t e d a b s o r p t i o n s removed. These are presented i n Table 6.7. The r e g r e s s i o n r e s u l t s f o r the o v e r a l l model are not as good as without vacancy r a t e s . F u r t h e r , the vacancy v a r i a b l e i s only m a r g i n a l l y s i g n i f i c a n t i n the equation f o r 1971 to 1983 with a b s o r p t i o n s , but f l i p s s i g n s when a b s o r p t i o n s are removed. These r e s u l t s suggest -that v a c a n c i e s , i n i s o l a t i o n , are an inadequate and u n r e l i a b l e i n d i c a t o r of a c t i v i t y i n the m u l t i f a m i l y housing market. 6.3 TIME SERIES MODEL Time s e r i e s models developed with the ARIMA process are based on the previous values f o r the estimated s e r i e s and the e r r o r of the l a s t p r e d i c t e d v a l u e . 2 9 The v o l a t i l i t y of the multi f a m i l y housing s t a r t s s e r i e s and p r e v i o u s work on dev e l o p i n g a time s e r i e s model f o r housing suggests that the a p p l i c a t i o n of ARIMA models to m u l t i f a m i l y s t a r t s w i l l be l i m i t e d . A time T a b l e 6.7 R e g r e s s i o n R e s u l t s - M u l t i F a m i l y H o u s i n g S t a r t s I n c l u d i n g Vacancy Rates CONSTANT VMFST1 ABSPRED VMFINV1 VVAC1 02 Q3 04 R' SE/DW 1963- 1980 1 176 0. 256 0 .682 -0 .277 15.996 157.46 274.38 406.74 . 348 643. .43 (2. 120) (2 .996) (1 .773) (0.295) (0.694) • (1.204) (1.829) .276 2 . 00 2 691 0. 429 -0. . 101 36.879 257.95 422.46 528.11 .256 682 . 34 (3. .813) (0. .640) (0.648) (1.085) (1.790) (2.278) . 186 2. 19 1971- 1980 3 -47 -0. 104 1 . 673 -0. 514 -192.08 -243.23 -234.80 216.61 .454 514 . 24 (0. 547) (3 125) (2. 355) ( 1 .462) (0.889) (0.787) (0.755) .334 2 . 12 4 687 0. 281 -o. 002 115.79 106.21 237.84 677.74 .287 578 . 52 (1. 737) (0. 01 1 ) (1.184) (0.378) (0.823) ( 1 737) . 157 2. 22 Notes: (1) t - s t a t 1 s t l c s In p a r e n t h e s i s (2) a '1' a f t e r the v a r i a b l e name i n d i c a t e s t h a t the v a r i a b l e i s l a g g e d one p e r i o d (3) R' v a l u e s r e p o r t e d a r e : f i r s t the u n a d j u s t e d R', and second the a d j u s t e d R' (4) SE/DW denotes the s t a n d a r d e r r o r and Durbln-Watson s t a t i s t i c 1 03 s e r i e s model has been developed to p rovide a comparison and to a i d i n t e s t i n g the r e l i a b i l i t y of the s t r u c t u r a l model. D i s c u s s i o n w i l l be l i m i t e d to a b r i e f o u t l i n e of the model de s i g n , with the r e s u l t s presented in Table 6.8. M u l t i f a m i l y s t a r t s data from 1963:1 to 1980:4 were used to estimate the time s e r i e s model. S t a t i o n a r i t y was acheived with f i r s t d i f f e r e n c e s . Two models were d e r i v e d from the d i f f e r e n c e d s e r i e s ; one based on an a u t o r e g r e s s i v e term and a moving average term, and the second based on these p l u s seasonal a u t o r e g r e s s i v e and moving average terms. Seasonal d i f f e r e n c i n g and second order d i f f e r e n c i n g were t e s t e d but the r e s u l t s i n d i c a t e d that the r e s u l t a n t s e r i e s were o v e r - d i f f e r e n c e d . A d d i t i o n a l parameters were added but were not s i g n i f i c a n t . F i n a l l y , s i n c e the s t r u c t u r a l model supported the p o s s i b i l i t y of a change in the s t r u c t u r e of the s t a r t s s e r i e s , another time s e r i e s using only data f o r 1971 to 1980 was c o n s i d e r e d . From the a u t o c o r r e l a t i o n s and p a r t i a l a u t o c o r r e l a t i o n s i t was not p o s s i b l e to i d e n t i f y a model. Recognizing that . f o r t y data p o i n t s may be i n s u f f i c i e n t to estimate a time s e r i e s model, t h i s was not pursued. The success of the time s e r i e s model, as i t compares to the s t r u c t u r a l model, w i l l be d i s c u s s e d i n the next s e c t i o n on f o r e c a s t i n g and t e s t measures. 6.4 FORECASTS AND TESTS OF MODEL RELIABILITY The f i n a l step of the a n a l y s i s i s to choose the optimal e s t i m a t i o n of the s t r u c t u r a l model and measure the a b i l i t y to Table 6.8 Time Series Models 1 04 Model 5 Autoregressive Terms Lag 1 4 0.2103 (1.262) Moving Average Terms 1 4 0.7966 (7.854) Residual Var iance 0.49771 * 106 0.3712 0.7900 (3.065) (4.311) 0.9597 0.62987 0.46684*106 (23.785) (3.0089) Note: t - s t a t i s t i c s in parenthesis 105 p r e d i c t t h e l e v e l o f m u l t i f a m i l y h o u s i n g s t a r t s b o t h w i t h i n a n d o u t s i d e t h e e s t i m a t i o n p e r i o d . The c o e f f i c i e n t s f o r t h e s t r u c t u a l m o d e l a r e f a i r l y s t a b l e s o t h e r e i s l i t t l e c o n c e r n t h a t t h e c h o s e n m odel w i l l n o t a c c u r a t e l y r e f l e c t t h e e s t i m a t i o n c a p a b i l i t i e s o f t h e m o d e l . However, t h e r e were some c h a n g e s when o n l y t h e 1971 t o 1980 d a t a was u s e d f o r t h e r e g r e s s i o n a n a l y s i s . T h e r e f o r e , f o u r e q u a t i o n s f r o m t h e r e g r e s s i o n r e s u l t s h a v e been c h o s e n t o m e a s u r e t h e r e l i a b i l i t y o f t h e p r o p o s e d m o d e l ; two f r o m t h e 1963-1980 r e s u l t s a n d t h e e q u i v a l e n t e q u a t i o n s f r o m t h e 1971-1980 r e s u l t s . T h e s e w i l l i n c l u d e e q u a t i o n 3 ( t h e b e s t o v e r a l l m o d e l ) a n d e q u a t i o n 5 w h i c h i s i d e n t i c a l , w i t h t h e a d d i t i o n o f t h e dummy t o remove t h e i m p a c t of t h e u n u s u a l d a t a i n 1977 a n d 1978. As m e n t i o n e d , t i m e s e r i e s m o d e l s have been d e v e l o p e d a s a c o m p a r a t i v e f o r t h e s t r u c t u r a l m o d e l . I n a d d i t i o n , a n a i v e s e r i e s h a s been c o n s t r u c t e d on t h e a s s u m p t i o n t h a t t h e b e s t f o r e c a s t i s t h e a c t u a l l e v e l o f s t a r t s i n t h e p r e v i o u s p e r i o d . I n summary, t h e f o l l o w i n g m o d e l s w i l l be t e s t e d : M o d e l 1 E q u a t i o n 3, T a b l e 6.4 M o d e l 2 E q u a t i o n 5, T a b l e 6.4 M o d e l 3 E q u a t i o n 3, T a b l e 6.6 M o d e l 4 E q u a t i o n 5, T a b l e 6.6 M o d e l 5 Time s e r i e s , a u t o r e g r e s s i v e a n d m o v i n g a v e r a g e t e r m s M o d e l 6 Time s e r i e s , n o n - s e a s o n a l a n d s e a s o n a l a u t o r e g r e s s i v e a n d m o v i n g a v e r a g e t e r m s M o d e l 7 N a i v e m o d e l , p r e v i o u s v a l u e I t i s i m p o r t a n t t o r e c o g n i z e t h a t t h e t i m e s e r i e s m o d e l s h a v e o n l y one l a g g e d p a r a m e t e r and t h e r e f o r e r e q u i r e i n f o r m a t i o n on t h e p r e c e d i n g p e r i o d t o f o r e c a s t t h e n e x t p e r i o d . T h e r e f o r e , t h e f o r e c a s t i n g a b i l i t y i s l i m i t e d t o one p e r i o d . S i m i l a r 106 r e s t r i c t i o n s a r e i n e f f e c t f o r t h e s t r u c t u r a l m o d e l s i n c e i t r e q u i r e s t h e c u r r e n t l e v e l o f i n v e n t o r y a n d t h e p r e v i o u s l e v e l o f s t a r t s t o f o r e c a s t f o r t h e n e x t p e r i o d . When p r e p a r i n g t h e f o r e c a s t e d s e r i e s f o r a l l o f t h e m o d e l , i t was'assumed t h a t t h i s d a t a w o u l d be a v a i l a b l e . T h a t i s , t h e f o r e c a s t e d m e a s u r e s o u t s i d e t h e e s t i m a t i o n p e r i o d a r e f o r one p e r i o d f o r w a r d and assume t h a t t h e a c t u a l l e v e l s f o r t h e p r e c e d i n g p e r i o d a r e a v a i l a b l e . 3 0 The p r e d i c t i o n r e s u l t s f o r t h e s e v e n m o d e l s g i v e n i n T a b l e 6.9 a r e d i v i d e d i n t o t h r e e p e r i o d s ; 1963 t o 1982, t h e s t u d y p e r i o d ; 1963 t o 1980, t h e e s t i m a t i o n p e r i o d ; a n d 1981 t o 1982, t h e f o r e c a s t p e r i o d . F o r e a c h t i m e p e r i o d t h e r e p o r t e d s t a t i s t i c s i n c l u d e t h e r o o t mean s q u a r e e r r o r (RMSE), mean a b s o l u t e e r r o r (MAE) a n d T h e i l U s t a t i s t i c . 3 1 The most i m p o r t a n t r e s u l t s a r e w i t h i n t h e e s t i m a t i o n p e r i o d a n d t h e f o r e c a s t p e r i o d . The r e s u l t s f o r 1963 t o 1980 s u g g e s t t h a t t h e s t r u c t u r a l m o d e l i s s u p e r i o r . The p r e f e r r e d e q u a t i o n i s more d i f f i c u l t t o i d e n t i f y s i n c e t h e RMSE i s h i g h e r f o r M o d e l s 1 and 2, b u t , t h e MAE i s h i g h e r f o r M o d e l s 3 and 4. S i n c e t h e RMSE p e n a l i z e s t h e f o r l a r g e e r r o r s , t h e p e r f o r m a n c e o f M o d e l s 3 a n d 4 w o u l d a p p e a r s l i g h t l y b e t t e r . 3 2 The r e s u l t s f o r t h e f o r e c a s t p e r i o d seem t o c a s t d o u b t on t h e r e l i a b i l i t y o f t h e s t r u c t u r a l m o d e l , e s p e c i a l l y i n c o m p a r i s o n t o t h e t i m e s e r i e s m o d e l . The p e r f o r m a n c e o f t h e n a i v e m o d e l i m p r o v e s , b u t , i t i s s t i l l o u t p e r f o r m e d by t h e o t h e r s e r i e s a n d w i l l n o t be d i s c u s s e d f u r t h e r . B e f o r e d i s m i s s i n g t h e f o r e c a s t i n g a b i l i t y o f t h e s t r u c t u r a l m o d e l i n f a v o u r o f t h e 1 07 TABLE 6.9 FORECASTING RESULT MEASURES MODEL 1 2 3 4 5 6 7 1963-1982 RMSE 862.603 812.668 820.021 766.560 966.528 1040.813 1318.178 MAE 514.968 477.948 600.529 599.504 577.935 583.734 641.564 THEIL 1.088 1.025 1.034 0.967 1.206 1.289 1.663 1963-1980 RMSE 881.687 825.011 825.212 774.948 1004.833 1086.575 1373.249 MAE 488.654 449.678 544.721 541.991 574.189 579.104 663.686 THEIL 1.079 1.009 1.010 0.948 1.214 1.301 1.680 1981-1982 RMSE 719.376 743.399 826.502 736.387 578.001 589.903 709.683 MAE 851.677 828.937 1244.401 1260.282 696.887 709.459 512.000 THEIL 1.265 1.307 1.454 1.295 1.017 1.037 1.248 108 t i m e s e r i e s m o d e l s an i m p o r t a n t p o i n t s h o u l d be c o n s i d e r e d . I t was n o t e d t h a t a l l o f t h e p r e d i c t i o n s were o n l y one p e r i o d f o r w a r d , s o t h e u n u s u a l a c t i v i t y i n t h e f o r e c a s t p e r i o d w o u l d be d e t e c t e d by t h e t i m e s e r i e s m o d el a n d n o t t h e s t r u c t u r a l m o d e l . N i n e t e e n - e i g h t y - o n e a n d 1982 were u n u s u a l y e a r s f o r t h e m u l t i f a m i l y m a r k e t w i t h t h e r e m o v a l o f t h e MURB p r o g r a m a s o f December 3 1 , 1981. The announcement o f t h e d i s c o n t i n u a t i o n o f t h e MURB p r o g r a m i n i t i a t e d an a b n o r m a l number o f s t a r t s a s b u i l d e r s o r i n v e s t o r s a t t e m p t e d t o c o n s t r u c t f o o t i n g s f o r f u t u r e p r o j e c t s a n d t h e r e b y q u a l i f y f o r t h e t a x b e n e f i t s a s s o c i a t e d w i t h MURBs. W i t h o u t b u i l d i n g a dummy t o c a p t u r e t h i s i m p a c t , t h e s t r u c t u r a l m o d el i s u n a b l e t o d e t e c t t h e u n u s u a l m a r k e t a c t i v i t y . The c o e f f i c i e n t o f s u c h a dummy c a n n o t be d e t e r m i n e d w i t h o u t f u r t h e r r e g r e s s i o n a n a l y s i s . The r e s u l t s w o u l d a p p e a r m i x e d . The r e s u l t s d u r i n g t h e e s t i m a t i o n p e r i o d s u p p o r t t h e i n v e n t o r y a d j u s t m e n t a p p r o a c h a n d i n d i c a t e t h a t t h e s t r u c t u r a l m o d e l i s s u p e r i o r t o t h e t i m e s e r i e s m o d e l . However, f o r f o r e c a s t i n g , t h e t i m e s e r i e s m o d e l p e r f o r m s b e t t e r d u r i n g 1981 and 1982. The d i f f i c u l t y w i t h t h e r e p o r t e d s t a t i s t i c a l t e s t s i s t h a t t h e y do n o t i n d i c a t e i f t h e m o d e l i s m i s s i n g t u r n i n g p o i n t s o r n o t m e a s u r i n g t h e e x t r e m e p o i n t s ; t h e n a t u r e o f t h e e r r o r s c a n n o t be d e t e r m i n e d . To f u r t h e r e v a l u a t e t h e p e r f o r m a n c e o f t h e m o d e l s , p l o t s o f t h e p r e d i c t e d a n d a c t u a l s e r i e s a r e p r e s e n t e d i n F i g u r e s 6.3 t h r o u g h 6.5. The s t r u c t u r a l m o d e l i s g e n e r a l l y s u c c e s s f u l i n d e t e r m i n i n g t h e t r e n d s i n t h e d a t a , b u t d o e s n o t r e a c h t h e e x t r e m e v a l u e s Figure 6.3 PREDICTED MULTI FAMILY HOUSING STARTS MODEL 2 actual series J 1 1 1 i i i i i i i i i i i i 1 1 1 1 1964 1966 1968 1970 1972 1974 1 976 1 978 1 980 1982 Units 4,000 L 3,000 \- 2,000 \- 1,000 Figure 6.4 PREDICTED MULTI FAMILY HOUSING STARTS MODEL 4 actual s e r i e s predicted s e r i e s 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 Units 5,000 4,000 \- 3,000 2,000 1,000 ir 1964 1966 1968 Figure 6.5 PREDICTED MULTI FAMILY HOUSING STARTS MODEL 5 actual series predicted series I i » I I L 1970 1972 1974 J I l_ I I I 1 1 1976 1978 1980 1982 1 12 e v i d e n t i n t h e a c t u a l s t a r t s s e r i e s . A l t h o u g h t h e l a g g e d s t a r t s e n t e r t h e e s t i m a t i o n o f t h e s e s e r i e s , t h e r e i s no measurement o f t h e p r e d i c t i o n e r r o r . T h e r e f o r e , i f some u n u s u a l f o r c e , s u c h a s a c h a n g e i n g o v e r n m e n t p o l i c y , d i s r u p t s t h e m a r k e t , t h e s t r u c t u r a l m o d e l w i l l be u n a b l e t o d e t e c t t h e c h a n g e a n d a d j u s t a c c o r d i n g l y . A l t e r n a t i v e l y , t h e t i m e s e r i e s m o d e l d e p e n d s upon s e r i a l c o r r e l a t i o n i n t h e s e r i e s f o r p r e d i c t i o n s . F o r h o u s i n g s t a r t s i t i s u n a b l e t o d e t e r m i n e t h e t u r n i n g p o i n t s , b u t i s s u c c e s s f u l i n p e r i o d s where t h e t r e n d i s s u s t a i n e d f o r s e v e r a l p e r i o d s . The a p p a r e n t f o r e c a s t i n g s u c c e s s o f t h e t i m e s e r i e s m o d e l i n 1981 and 1982 i s o b v i o u s l y b e n e f i t t i n g f r o m s u c h a p a t t e r n . The model d o e s n o t d e t e c t t h e t u r n i n g p o i n t s w i t h i n t h e e s t i m a t i o n p e r i o d and f a i l s i n p r e d i c t i n g t h e i n i t i a l i n c r e a s e o r d e c l i n e i n s t a r t s i n t h e f o r e c a s t i n g p e r i o d . The s t a b i l i t y o f t h e c o e f f i c i e n t s i n t h e r e g r e s s i o n a n a l y s i s f o r t h e s t a r t s m o d el a n d t h e a b i l i t y o f t h e m o d e l t o o u t p e r f o r m a t i m e s e r i e s m o d e l d u r i n g t h e e s t i m a t i o n p e r i o d s u g g e s t t h a t t h e p r o p o s e d a p p r o a c h may be a b l e t o p r o v i d e r e a s o n a b l e m a r k e t p r e d i c t i o n s . C o n s i d e r i n g t h e a b n o r m a l m a r k e t c o n d i t i o n s i n 1981, t h e l a c k o f f o r e c a s t i n g s u c c e s s d o e s n o t c r e a t e any g r e a t c o n c e r n . I t may be u s e f u l t o f u r t h e r d e v e l o p t h e m o d e l t o i n c o r p o r a t e a t i m e s e r i e s a s w e l l , t h e r e b y p e r m i t t i n g t h e c o m p l e t e m o d e l t o b e n e f i t f r o m i n f o r m a t i o n on i n v e n t o r i e s , e c o n o m i c c o n d i t i o n s a n d u n u s u a l m a r k e t b e h a v i o u r ; t h e f o r m e r t h r o u g h t h e s t r u c t u r a l v a r i a b l e s , t h e l a t t e r t h r o u g h t h e e r r o r t e r m o f t h e t i m e s e r i e s m o d e l . 1 13 7. CONCLUSIONS AND FUTURE RESEARCH T h i s s t u d y h a s p r o p o s e d t h e a d o p t i o n o f t h e i n v e n t o r y a d j u s t m e n t m o d e l t o e s t i m a t e a n d p r e d i c t m u l t i f a m i l y h o u s i n g s t a r t s . The t h e o r e t i c a l m o d e l s u g g e s t s t h a t t h e r e i s some d e s i r e d i n v e n t o r y l e v e l w h i c h b u i l d e r s o r i n v e s t o r s w i l l t r y t o m a i n t a i n d e p e n d i n g on e x p e c t e d p r o f i t a b i l i t y , t h e r e l a t i v e y i e l d on o t h e r i n v e s t m e n t s a n d t h e c o s t o f m a i n t a i n i n g v a c a n t u n i t s . Demand f o r new r e n t a l u n i t s w i l l d e p e n d upon t h e d e m o g r a p h i c s t r u c t u r e o f t h e p o p u l a t i o n , u n e m p l o y m e n t , i n c o m e , a n d t h e r e l a t i o n s h i p b e t w e e n r e n t s o w n e r s h i p c o s t s a n d t h e c o s t o f o t h e r g o o d s a n d s e r v i c e s . S t a r t s , o r p r o d u c t i o n , w i l l be s e t t o S a t i s f y t h e e x p e c t e d demand a n d a d j u s t a c t u a l i n v e n t o r y l e v e l s t o t h e d e s i r e d i n v e n t o r y l e v e l . T h i s i s i n c o n t r a s t t o t h e t r a d t i o n a l a p p r o a c h w h i c h s u g g e s t s t h a t v a c a n c y r a t e s a r e an i n d i c a t o r o f demand and d u r i n g p e r i o d s o f l o w v a c a n c i e s m u l t i f a m i l y h o u s i n g s t a r t s w i l l i n c r e a s e . Q u a r t e r l y d a t a f o r t h e V a n c o u v e r CMA, f r o m 1963:1 t o 1982:4 has b een u s e d t o d e v e l o p a n d t e s t a s t r u c t u r a l model b a s e d on t h e i n v e n t o r y a d j u s t m e n t a p p r o a c h . The a v a i l a b l e d a t a p o s e d p r o b l e m s i n e s t i m a t i n g t h e c h a n g e i n t h e number o f t o t a l a n d r e n t a l h o u s e h o l d s . A l s o , t h e a p a r t m e n t s e r i e s f o r s t a r t s a n d i n v e n t o r i e s i n c l u d e s g o v e r n m e n t p r o j e c t s , w h i c h do n o t r e s p o n d t o t h e same m a r k e t f o r c e s a s p r i v a t e l y i n i t i a t e d c o n s t r u c t i o n , a n d c o n d o m i n i u m s , w h i c h a r e n o t n e c e s s a r i l y p a r t o f t h e r e n t a l s t o c k . The m o d e l r e s u l t s y i e l d an a d j u s t e d R 2 o f a b o u t 0.3 1 14 ( d e p e n d i n g on t h e s p e c i f i c a t i o n ) . S e v e r a l p o i n t s s u g g e s t t h a t t h e m o d e l may w a r r a n t f u r t h e r i n v e s t i g a t i o n . As was n o t e d p r e v i o u s l y , t h e s i z e o f m u l t i f a m i l y p r o j e c t s w i l l i n f l u e n c e t h e a p p e a r a n c e o f t h e d a t a s e r i e s a n d may b i a s t h e r e s u l t s . A l s o , by u s i n g r e g i o n a l d a t a , t h e r e may be some c o l l e c t i o n e r r o r w h i c h i s m i n i m i z e d by a g g r e g a t i n g t o t h e n a t i o n a l l e v e l . V a c a n c y r a t e s were i n s i g n i f i c a n t when i n c l u d e d i n t h e r e g r e s s i o n e s t i m a t i o n s s u g g e s t i n g t h a t t h e y a r e n o t a c o m p l e t e i n d i c a t o r o f demand and may n o t be a m a j o r d e t e r m i n a n t i n c o n s t r u c t i o n d e c i s i o n s . I n v e n t o r i e s do e n t e r t h e r e s u l t s w i t h a s i g n i f i c a n t n e g a t i v e c o e f f i c i e n t , a s e x p e c t e d . P l o t s o f t h e p r e d i c t e d a n d r e a l i z e d s e r i e s i n d i c a t e t h a t t h e m o d e l i s s u c c e s s f u l i n d e t e c t i n g t h e t r e n d s i n s t a r t s , a l t h o u g h i t d o e s n o t a t t a i n t h e same e x t r e m e v o l a t i l i t y a s t h e a c t u a l s e r i e s . P r e d i c t i o n s f o r 1981 and 1982 u s i n g t h e r e g r e s s i o n r e s u l t s a r e u n a b l e t o a c c u r a t e l y m o n i t o r t h e m a r k e t a c t i v i t y . S i n c e t h e h i g h l e v e l o f s t a r t s i n t h i s p e r i o d i s t h e r e s u l t o f d i s c o n t i n u a t i o n o f MURB b e n e f i t s , t h i s i s i n s u f f i c i e n t e v i d e n c e t o d i s c o u n t t h e m o d e l . I n a n s w e r t o t h e q u e s t i o n s p o s e d a t t h e o u t s e t , i t w o u l d a p p e a r t h a t i n v e n t o r i e s , t h e c o s t o f m a i n t a i n i n g i n v e n t o r y a n d t h e e x p e c t e d demand h a v e c o n t r i b u t e d t o t h e d e c l i n e i n s t a r t s t h r o u g h o u t t h e 1970 ' s . To c o n c l u d e t h a t v a c a n c y r a t e s h a v e no i m p a c t a n d t h a t t h e v o l a t i l i t y o f s t a r t s i s a t t r i b u t a b l e t o an i n v e n t o r y c y c l e i s t o o s t r o n g g i v e n t h e e v i d e n c e p r e s e n t e d i n t h i s p a p e r . The r e s u l t s do s u p p o r t t h e i n v e n t o r y a p p r o a c h , b u t , d a t a d i f f i c u l t i e s i n e s t i m a t i n g t h e e m p i r i c a l m o d e l a r e 1 1 5 s u f f i c i e n t t o p r o h i b i t s u c h a d e c i s i v e c o n c l u s i o n . B e f o r e t h e a p p l i c a t i o n o f t h e i n v e n t o r y a d j u s t m e n t a p p r o a c h t o m u l t i f a m i l y h o u s i n g c a n be d i s c o u n t e d o r a r g u e d more s t r o n g l y , a c o u p l e o f c o n s i d e r a t i o n s s h o u l d be a d d r e s s e d . I s V a n c o u v e r t y p i c a l o f C a n a d i a n u r b a n c e n t r e s , o r a r e t h e s u c c e s s e s o r f a i l i n g s o f t h e s e r e s u l t s c a u s e d by i d i o s y n c r a c i e s o f t h e V a n c o u v e r h o u s i n g m a r k e t ? S t u d i e s o f s i n g l e f a m i l y h o u s i n g p r i c e s s u g g e s t t h a t t h e V a n c o u v e r m a r k e t i s u n i q u e . A c r o s s - s e c t i o n a l a n a l y s i s , u s i n g o t h e r C a n a d i a n u r b a n c e n t r e s t o e s t i m a t e s i m i l a r e q u a t i o n s , i s n e e d e d t o d e t e r m i n e t h e u n i q u e n e s s of t h e s e r e s u l t s . A l s o , t h e i m p o r t a n c e o f m a r k e t s u b s t i t u t e s s u c h a s c o n v e r s i o n s a n d c o n d o m i n i u m s n e e d s t o be i n v e s t i g a t e d and i n c o r p o r a t e d i n t o t h e r e s u l t s . I t w o u l d a p p e a r t h a t l e g a l and i l l e g a l s u i t e s have p r o v i d e d an a l t e r n a t e f o r m o f r e n t a l a c c o m o d a t i o n b u t have n o t been i n c l u d e d s i n c e t h e d a t a was n o t a v a i l a b l e . C o n d o m i n i u m s may be r e n t e d upon c o m p l e t i o n even i f a s t r a t a t i t l e i s o b t a i n e d f o r t h e p r o j e c t l e a d i n g t o i n c o n s i s t e n t d a t a on s t r u c t u r e and t e n u r e t y p e s . I t i s no l o n g e r v a l i d t o assume t h a t a p a r t m e n t o r m u l t i f a m i l y s t r u c t u r e s a r e r e n t a l . G o v e r n m e n t i n t e r v e n t i o n i n t h e h o u s i n g m a r k e t h a s c l o u d e d i n t e r p r e t a t i o n o f t h e r e s u l t s . P o l i c y h a s been t o e n c o u r a g e home o w n e r s h i p . P r o g r a m s i n t r o d u c e d t h r o u g h o u t t h e 1970's and t h e i n a b i l i t y t o model t h e i r i m p a c t s s u g g e s t t h a t t h e m a r k e t has b e en d i s r u p t e d . The p r e c i s e i m p l i c a t i o n s on t h e r e s u l t s and f u t u r e p r e d i c t i o n s c a n n o t be m e a s u r e d . C l e a r l y , t h e i n a b i l i t y o f t h e m o d el t o f o r e c a s t f o r 1981 a n d 1982 i s t h e r e s u l t of t h e 116 MURB p r o g r a m , b u t i t i s i m p o s s i b l e t o m o n i t o r t h e s e i m p a c t s i n a d v a n c e , and i m p r o v e t h e f o r e c a s t i n g c a p a b i l i t i e s o f t h e m o d e l . F u t u r e r e s e a r c h may be a b l e t o b e n e f i t f r o m i m p r o v e d d a t a c o l l e c t i o n . S t a r t i n g i n 1981, CMHC r e p o r t s s t a r t s a n d i n v e n t o r i e s by s o u r c e o f f u n d s a n d t e n u r e t y p e . I t may t h e n be p o s s i b l e t o r e - e s t i m a t e t h e i n v e n t o r y a d j u s t m e n t m o del f o r o n l y t h e p r i v a t e l y i n i t i a t e d r e n t a l component o f t h e m u l t i f a m i l y h o u s i n g m a r k e t , a s p r o p o s e d i n t h e t h e o r e t i c a l m o d e l . The r e s u l t s p r e s e n t e d s u g g e s t t h a t t h e a p p r o a c h i s a p p r o p r i a t e , b u t , t h e d a t a i n a d e q u a c i e s h a v e l i m i t e d t h e s i g n i f i c a n c e a n d r e l i a b i l i t y o f t h e r e s u l t s . F u r t h e r c r o s s - s e c t i o n a l a n a l y s i s may p r o v i d e more i n f o r m a t i o n on t h e s u c c e s s o f t h e p r o p o s e d t e c h n i q u e . A l s o , t h e i n c o r p o r a t i o n o f a t i m e s e r i e s m o d el w i t h t h e r e g r e s s i o n a n a l y s i s may be j u s t i f i e d t o m o n i t o r p r e d i c t i o n e r r o r s and i n c o r p o r a t e t h e s e i n t h e f o r e c a s t s . 1 1 7 NOTES 1. F o r a f u r t h e r d i s c u s s i o n o f t h i s p o i n t s e e A l b e r t s , 1962; G u t t e n t a g , 1961; S m i t h , 1 9 7 4 , p p 3 l - 3 5 . 2. P r i o r l o a n c o m m i t m e n t s w i l l be e s p e c i a l l y i m p o r t a n t f o r c o n s t r u c t i o n l o a n s on l a r g e p r o j e c t s where a r r a n g e m e n t s a r e u s u a l l y made p r i o r t o t h e commencement o f c o n s t r u c t i o n . 3. See G r e b l e r & M a i s e l , 1963; S m i t h , 1974; S t e v e n s , 1 9 7 6 ; S t e e l e , 1 9 7 9 . 4. I n r e s p o n s e t o p a p e r p r e s e n t e d by Q u i g l e y , 1978. See B o u r n e & H i t c h c o c k , U r b a n H o u s i n g M a r k e t s : R e c e n t D i r e c t i o n s i n R e s e a r c h a n d P o l i c y . 5. F o r more c o m p l e t e d i s c u s s i o n s o f C a n a d i a n h o u s i n g p o l i c y a n d i t s i m p l i c a t i o n s , see D a l e - J o h n s t o n , 1977; F a l l i s , 1981; Gau & W i c k s , 1982; G o l d b e r g , 1983; Heung, 1976; J o n e s , 1983; S m i t h , 1 9 77,1981,1982; W i c k s , 1982. 6. W i t h t h i s amendment, m u l t i f a m i l y s t r u c t u r e s where t h e owner was r e s i d e n t , o r c o m m e r c i a l s t r u c t u r e s where t h e r e was a r e s i d e n c e a t t a c h e d , q u a l i f i e d f o r t h e s e g r a n t s . 7. NHA m o r t g a g e s r e q u i r e t h a t t h e downpayment be u n e n c u m b e r e d . 8. Rent c o n t r o l s a n d t h e i m p a c t on t h e m a r k e t h a s been a c o n t r o v e r s i a l i s s u e t h r o u g h o u t t h e 1970' s . A r g u m e n t s on c o n t r o l s a r e p r e s e n t e d i n J o n e s , 1983; S m i t h & T o m l i n s o n , 1 9 8 1 . 9. Z o n i n g a n d i t s i m p l i c a t i o n s f o r V a n c o u v e r a r e d i s c u s s e d i n Heung, 1976; J a f f a r y , e t a l . , 1975; G o l d b e r g & Horwood, 1980. 10. F o r a d i s c u s s i o n on i n f l a t i o n a n d h o u s i n g see C a p o z z a , 1983; D o u g h t e r t y a n d Van O r d e r , 1982; G o l d b e r g , 1983; H e n d e r s h o t t , 1980; K e a r l , 1979. 11. see Cameron & J o h n s t o n , 1 9 8 1 . 12. see Gau & W i c k s , 1982; W i c k s , 1982. 13. F o r a c o m p l e t e d i s c u s s i o n o f t h e i n v e n t o r y c o n c e p t and t h e d e r i v a t i o n o f t h e m o d e l s e e M e l t z e r , 1940; A l l e n , 1957; L o v e l l , 1966. 14. The a g e - s e x b r e a k d o w n a nd r e n t a l demand f o r t h e age c o h o r t w i l l be u s e d t o d e t e r m i n e t h e f u t u r e r e n t a l demand a s t h e p o p u l a t i o n a g e s . The r a t e o f h o u s e h o l d f o r m a t i o n may be a c c e l e r a t e d o r d e l a y e d d e p e n d i n g on e c o n o m i c c o n d i t i o n s . When t h e g e n e r a l e c o n o m i c c o n d i t i o n s a r e f a v o u r a b l e , a n i n c r e a s e i n h o u s e h o l d f o r m a t i o n i s e x p e c t e d . 15. T h i s i s s i m i l a r t o t h e l a n d v a l u a t i o n f u n c t i o n u s e d by 1 18 W i c k s , 1982. 16. T h i s method o f p r o j e c t i n g t h e number o f r e n t a l h o u s e h o l d s i s s i m i l a r t o t h e a p p r o a c h e d p r o p o s e d by J a f f e e & R o s e n ( 1 9 7 9 ) t o p r o j e c t t h e d e m o g r a p h i c demand f o r s i n g l e f a m i l y u n i t s . 17. See S t a t i s t i c s C a n a d a , C a t o l d g u e 62-010, Consumer P r i c e s a n d P r i c e I n d e x e s f o r an e x p l a n a t i o n o f t h e c o n v e r s i o n t e c h n i q u e and c h a n g e s i n t h e b a s k e t o f g o o d s . 18. See d e f i n i t i o n s o u t l i n e d i n S t a t i s t i c s C anada C a t a l o g u e 64- 002, p p 5 - 6 . 19. See A p p e n d i x B f o r a l i s t i n g o f t h e c o m p l e t e d a t a s e r i e s . 20. F i r s t d i f f e r e n c e s w i l l e l i m i n a t e t h e p r o b l e m s o f t r e n d s , h o w e v e r , i f t h e e q u a t i o n s a r e e s t i m a t e d f o r t h e c h a n g e s , n o t t h e o r i g i n a l l e v e l s , a u t o c o r r e l a t i o n w i l l be i n t r o d u c e d i n t o t h e r e s u l t s i f t h e o r i g i n a l d a t a i s s e r i a l l y i n d e p e n d e n t . A common s c a l i n g f a c t o r w i l l a l s o r e d u c e t h e t r e n d , b u t t h e r e s i d u a l s w i l l t h e n be h e t e r o s c e d a s t i c a n d t h e r e i s t h e p o s s i b i l i t y o f " s p u r i o u s " c o r r e l a t i o n f r o m t h e s c a l i n g v a r i a b l e . Where d a t a i s i n s u f f i c i e n t t o p e r m i t a c c u r a t e measurement o f t h e i m p a c t s o f e a c h i n d e p e n d e n t v a r i a b l e , a n d more d a t a c a n n o t be c o l l e c t e d , i t may be n e c e s s a r y t o o m i t some v a r i a b l e s f r o m t h e e q u a t i o n t o r e d u c e t h e m u l t i c o l l i n e a r i t y . I f i t i s n o t n e c e s s a r y t o ha v e a p r e c i s e c o e f f i c i e n t f o r e a c h i n d e p e n d e n t v a r i a b l e , t h i s i s t h e p r e f e r r e d a p p r o a c h . 21. The dummy, v a r i a b l e i s e q u a l t o z e r o where unemployment d a t a i s a v a i l a b l e ( 1 9 6 6 - 1 9 8 2 ) a nd one where d a t a i s m i s s i n g ( 1 9 6 3 - 1 9 6 5 ) . 22. S i n c e t h e dummy v a r i a b l e i s one when t h e p r o g r a m i s NOT i n e f f e c t a n d t h e s e y e a r s w o u l d be e x p e c t e d t o ha v e a h i g h e r number of a b s o r p t i o n s i f home o w n e r s h i p i s e n c o u r a g e d , t h e s i g n s h o u l d be p o s i t i v e . 23. L o g s a n d a b s o r p t i o n s a s a p e r c e n t a g e o f s t o c k were t r i e d w i t h o u t any i m p r o v e m e n t i n t h e s p e c i f i c a t i o n o r t h e e l i m i n a t i o n of t h e s e p r o b l e m s . 24. T h i s d a t a was c h o s e n b a s e d on t h e i n c r e a s i n g g o v e r n m e n t p r o g r a m s i n t h e 1970's a n d t h e e x t e n s i v e c h a n g e s i n t a x l e g i s l a t i o n i n t h e e a r l y 1 9 7 0 ' s . 25. The p r o x y f o r p r o f i t w h i c h y i e l d e d t h e b e s t r e s u l t s i s t h e r e n t a l CPI d e f l a t e d by t h e c o n s t r u c t i o n c o s t i n d e x . O t h e r m e a s u r e s d e r i v e d t o i n c o r p o r a t e t h e v a c a n c y r a t e o r i n t e r e s t r a t e were l e s s s u c c e s s f u l t h a n t h e s i m p l i s t i c m e a s u r e u s e d . A l t e r n a t e m e a s u r e s s u c h a s t h e r a t e o f r e t u r n s e r i e s d e r i v e d by Gau ( 1 9 8 3 ) may p r o v e more a c c u r a t e . P a r t o f t h e i n t e n t o f t h i s s t u d y i s t o use r e a d i l y a c c e s s i b l e d a t a t o p e r m i t c r o s s - s e c t i o n a l a n a l y s i s w i t h o t h e r C a n a d i a n c e n t r e s . T h e r e f o r e , 119 t h e s e a l t e r n a t e m e a s u r e s were n o t p u r s u e d . 26. A dummy v a r i a b l e was s p e c i f i e d a s '1* b e f o r e 1972 a n d ' 1 ' d u r i n g t h e p e r i o d when t h e MURB p r o g r a m was i n p l a c e , a n d z e r o o t h e r w i s e . The r e s u l t s d i d n o t c o n t r i b u t e t o t h e a d j u s t e d R 1, o r r e d u c e t h e s t a n d a r d e r r o r . A t t e m p t s were a l s o made t o r e p l i c a t e t h e l a g g e d e f f e c t o f s t a r t s a f t e r t h e p r o g r a m ' s i n c e p t i o n a n d a n n o u n c e d r e m o v a l . T h e s e a l s o f a i l e d . No d o u b t t h e p r o g r a m i n f l u e n c e d t h e m a r k e t , b u t t h e d e s i g n o f an a p p r o p r i a t e dummy v a r i a b l e c o u l d n o t be d e t e r m i n e d . The p e r i o d o f 1977-78 p o r t r a y e d an u n u s u a l d r o p i n s t a r t s . P a r t o f t h i s maybe a t t r i b u t a b l e t o t h e ARP p r o g r a m , b u t t h e e x a c t n a t u r e o f t h e d e c l i n e i s unknown (2000 s t a r t s t o 200 s t a r t s i n one q u a r t e r ) . To r e d u c e t h e i m p a c t o f t h i s p e r i o d on t h e o t h e r c o e f f i c i e n t s a dummy was u s e d w i t h t h e f o l l o w i n g v a l u e s : z e r o e x c e p t f o r : 1977:3 +1 1977:4 +2 1978:1 +3 1978:2 -3 1978:3 -2 1978:4 -1 Rem o v a l o f t h i s u n u s u a l p e r i o d i m p r o v e s t h e m o d e l r e s u l t s b u t w i l l be o f l i t t l e f o r e c a s t i n g v a l u e , e x p e c t p e r h a p s i n b e t t e r c o e f f i c i e n t e s t i m a t e s . 27. The e s t i m a t e d c o e f f i c i e n t f o r t h e a d j u s t m e n t p r o c e s s w i l l be (1-5$). The mean l a g i s t h e n ( l - f r ) A , o r . 258/( 1 -. 258) . 28. See S m i t h , 1976; J a f f e e & R o s e n , 1979; R o s e n , 1979; M a i s e l , 1963. 29. F o r a d i s c u s s i o n o f t h e s e t e c h n i q u e s s e e Box & J e n k i n s , 1976 o r M a d d a l a , 1977. 30. The a l t e r n a t i v e a s s u m p t i o n w o u l d be t o p r o j e c t v a l u e s f o r a l l t h e n e c e s s a r y v a r i a b l e s a n d u s e t h e p r o j e c t e d v a l u e s t o c a l c u l a t e t h e f o r e c a s t s . The r e l i a b i l i t y o f t h e s t r u c t u r a l m o d e l i s t h e n s u b j e c t t o t h e a c c u r a c y o f t h e p r o j e c t e d v a l u e s . F o r c o n s i s t e n c y i n c o m p a r i n g t h e t i m e s e r i e s a n d s t r u c t u r a l m o d e l t h i s a p p r o a c h i s n o t u s e d . 3 1 . See M a d d a l a , 1977 f o r a d e s c r i p t i o n o f t h e s e s t a t i s t i c s . 32. No d i s t i n c t i o n i s made b e t w e e n M o d e l s 1 a n d 2, a n d M o d e l s 3 and 4 s i n c e t h e o n l y d i f f e r e n c e i n t h e s e two e q u a t i o n s i s f o r 1977-78. T h e r e f o r e , w i t h i n t h e e s t i m a t i o n p e r i o d , r e m o v a l o f t h e u n u s u a l d a t a o f t h i s p e r i o d w i l l o b v i o u s l y i m p r o v e t h e r e s u l t s . What s h o u l d be c o n s i d e r e d i s t h e i m p a c t o f t h i s on t h e c o e f f i c i e n t s . I m p r o v e d c o e f f i c i e n t v a l u e s w i l l p r o v i d e a b e t t e r f o r e c a s t i n g m o d e l . 1 20 BIBLIOGRAPHY A l b e r t s , W i l l i a m W., 1962, " B u s i n e s s C y c l e s , R e s i d e n t i a l C o n s t r u c t i o n C y c l e s , a nd t h e M o r t g a g e M a r k e t " , J o u r n a l o f . P o l i t i c a l Economy , V o l 70, ( J u n e ) , p p 2 6 3 - 8 1 . A l l e n , R.D.G., 1957, M a t h e m a t i c a l E c o n o m i c s , L o n d o n : M a c M i l l a n & Co. L t d . A r c e l u s , F r a n c i s c o & A l l a n A. M e l t z e r , 1973, "The M a r k e t s f o r H o u s i n g a n d H o u s i n g S e r v i c e s " , J o u r n a l o f Money C r e d i t a n d B a n k i n g , ( F e b r u a r y ) , pp 78-99. B l i n d e r , A l a n S., 1982, " I n v e n t o r i e s and S t i c k y P r i c e s : More on t h e M i c r o f o u n d a t i o n s o f M a c r o e c o n o m i c s " The A m e r i c a n E c o n o m i c R e v i e w , V o l 72, No 3 ( J u n e ) pp 3 3 4 - 3 4 8 . B l i n d e r , A l a n S. & S t a n l e y F i s c h e r , 1981, " I n v e n t o r i e s R a t i o n a l E x p e c t a t i o n s , a n d t h e B u s i n e s s C y c l e " , J o u r n a l o f M o n e t a r y E c o n o m i c s , V o l 8 No3, (Nov) pp 2 7 7 - 3 0 4 . B o u r n e , L a r r y S., 1981, The G e o g r a p h y o f H o u s i n g L o n d o n : Edward A r n o l d ( P u b l i s h e r s ) L t d . B o u r n e , L a r r y S. & J o h n R. H i t c h c o c k ( e d ) , 1978, U r b a n H o u s i n g M a r k e t s : R e c e n t D i r e c t i o n s i n R e s e a r c h a n d P o l i c y , T o r o n t o : U n i v e r s i t y o f T o r o n t o P r e s s . B ox, G e o r g e E.P. & G w i l y m M. J e n k i n s , 1976, Time S e r i e s A n a l y s i s F o r e c a s t i n g a nd C o n t r o l , R e v i s e d E d i t i o n , San F r a n c i s c o : H o l d e n - D a y . B r a u n , S t e v e n , 1981, "The I n v e n t o r y S t o c k - A d j u s t m e n t M o d e l R e c o n s i d e r e d " , The R e v i e w of E c o n o m i c s and S t a t i s t i c s , V o l . 6 3 , No3. pp 452-54. B r e n n a n , M i c h a e l J . , 1959, "A M o d e l of S e a s o n a l I n v e n t o r i e s " E c o n o m e t r i c a , V o l 27, pp 228-244. Cameron, J.G. & K. J o h n s t o n , 1981, "An A n a l y s i s o f t h e M u l t i p l e U n i t R e s i d e n t i a l B u i l d i n g P r o g r a m " , p r e p a r e d f o r B.C. M i n i s t r y o f L a n d s , P a r k s and H o u s i n g , A u g u s t . C a p o z z a , D.R., 1983, "What Does i t C o s t t o Own a House i n C a n a d a ? " , R e s e a r c h i n U r b a n L a n d E c o n o m i c s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , WP No. 26. Chung, J.H., 1976, C y c l i c a l I n s t a b i l i t y i n R e s i d e n t i a l C o n s t r u c t i o n i n C a n a d a , O t t a w a : E c o n o m i c C o u n c i l o f C a n a d a . D a l e - J o h n s o n , D a v i d , 1976, "Government H o u s i n g P o l i c y a n d P r o g r a m s : T h e i r I m p a c t on H o u s i n g Demand i n B r i t i s h C o l u m b i a " , i n F r e d P e n n a n c e , e t a l . , H o u s i n g : I t s Y o u r Move V o l I I V a n c o u v e r : U r b a n L a n d E c o n o m i c s D i v i s i o n , F a c u l t y o f 121 Commerce a n d B u s i n e s s A d m i n i s t r a t i o n , U n i v e r s i t y o f B r i t i s h C o l u m b i a . D a v i e s , G o r d o n W., 1977, "A M o d e l o f t h e U r b a n R e s i d e n t i a l L a n d & H o u s i n g M a r k e t s " , C a n a d i a n J o u r n a l o f E c o n o m i c s V o l X, No 3 (Aug) pp 3 9 3 - 4 1 0 . deLeeuw, F r a n k & N k a n t a F. Ekanem, 1971, "The S u p p l y o f R e n t a l H o u s i n g " , The A m e r i c a n E c o n o m i c R e v i e w , V o l 6 1 , No 5, pp 8 0 6 - 8 1 7 . deLeeuw, F r a n k & N k a n t a F. Ekanem, 1973, "Time L a g s i n t h e R e n t a l H o u s i n g M a r k e t " , U r b a n S t u d i e s p p 3 9 - 6 8 . D o u g h e r t y , Ann & R o b e r t Van O r d e r , 1982, " I n f l a t i o n , H o u s i n g C o s t s , and t h e Consumer P r i c e I n d e x " , A m e r i c a n E c o n o m i c J o u r n a l V o l 72, No 1, ( M a r c h ) pp 154-164. E g e r , A.F., 1983, " F o r e c a s t i n g H o u s i n g S t a r t s i n C a n a d i a n C e n s u s M e t r o p o l i t a n A r e a s : A S t o c k A d j u s t m e n t A p p r o a c h U s i n g M o v i n g A v e r a g e s " , M c G i l l U n i v e r s i t y , W o r k i n g P a p e r 8 3 . F a i r , R . C , 1972, " D i s e q u i l i b r i u m i n H o u s i n g M a r k e t s " , The J o u r n a l o f F i n a n c e V o l 27 ( M a y ) . F a i r , R.C. & D.M. J a f f e e , 1972, "Methods o f E s t i m a t i o n f o r M a r k e t s i n D i s e q u i l i b r i u m " , E c o n o m e t r i c a V o l 40 No 3, (May) pp 4 97-514. F a l l i s , G e o r g e , 1981, "The N o r m a t i v e B a s i s o f H o u s i n g P o l i c y " , P a p e r P r e p a r e d f o r t h e Symposium on N o r t h A m e r i c a n H o u s i n g M a r k e t s i n t o t h e 2 1 s t C e n t u r y , UBC, ( J u l y ) . F e l d s t e i n , M a r t i n & A l a n A u e r b a c h , 1976, " I n v e n t o r y B e h a v i o u r i n D u r a b l e Goods M a n u f a c t u r i n g : The T a r g e t - A d j u s t m e n t M o d e l " , B r o o k i n g s P a p e r s on E c o n o m i c A c t i v i t y , no 2 pp 3 5 1 - 4 0 8 . F o l l a i n , James R., 1979, "A S t u d y o f t h e Demand f o r H o u s i n g by Low v e r s u s H i g h Income H o u s e h o l d s " , ( S e p t e m b e r ) . F o s t e r , E d w a r d , 1963, " S a l e s F o r e c a s t s a n d t h e I n v e n t o r y C y c l e " , E c o n o m e t r i c a V o l 3 1 , No 3 ( J u l y ) . Fromm, G a r y , 1973, " E c o n o m e t r i c M o d e l s o f t h e R e s i d e n t i a l C o n s t r u c t i o n S e c t o r : A C o m p a r i s o n " , i n R. B r u c e R i c k s (ed) N a t i o n a l H o u s i n g M o d e l s : A p p l i c a t i o n o f E c o n o m e t r i c T e c h n i q u e s t o P r o b l e m s o f H o u s i n g R e s e a r c h , L e x i n g t o n . Gau, G e o r g e W. & Anne P. W i c k s , 1982, " I m p a c t o f t h e ARP and MURB P r o g r a m s on t h e V a n c o u v e r H o u s i n g M a r k e t " , V a n c o u v e r : F a c u l t y o f Commerce, UBC, W o r k i n g P a p e r 14. 122 G o l d b e r g , M i c h a e l A., 1983, The H o u s i n g P r o b l e m : A R e a l C r i s i s ? , V a n c o u v e r : U n i v e r s i t y o f B r i t i s h C o l u m b i a P r e s s . G o l d b e r g , M i c h a e l A. & P e t e r Horwood, 1980, Z o n i n g : I t s C o s t s a n d R e l e v a n c e f o r t h e 1980s V a n c o u v e r : The F r a s e r I n s t i t u t e . G o l d b e r g , M i c h a e l A. & D a n i e l D. U l i n d e r , 1 9 7 6 , " R e s i d e n t i a l D e v e l o p e r B e h a v i o u r 1975: A d d i t i o n a l E m p i r i c a l F i n d i n g s " , L a n d E c o n o m i c s V o l 52, No 3 ( A u g ) . G r i e s o n , R o n a l d E., 1983, The U r b a n Economy and H o u s i n g T o r o n t o : L e x i n g t o n B o o k s . G r e b l e r , L e o & Sherman J . M a i s e l , 1963, " D e t e r m i n a n t s o f R e s i d e n t i a l C o n s t r u c t i o n : A R e v i e w o f P r e s e n t K n o w l e d g e " , i n D a n i e l B. S u i t s & o t h e r s , I m p a c t s o f M o n e t a r y P o l i c y , p r e p a r e d f o r t h e C o m m i s s i o n on Money & C r e d i t , P r e n t i c e - H a l l . G u t t e n t a g , J a c k M., 1961, "The S h o r t C y c l e i n R e s i d e n t i a l C o n s t r u c t i o n 1946-1956" , A m e r i c a n E c o n o m i c R e v i e w , V o l 51 ( J u n e ) p p 2 7 5 - 9 8 . H a n u s h e k , E.A. & J.M. Q u i g l e y , 1978, "The D y n a m i c s o f t h e H o u s i n g M a r k e t : A S t o c k A d j u s t m e n t M o d e l o f H o u s i n g - C o n s u m p t i o n " J o u r n a l o f U r b a n E c o n o m i c s . H e n d e r s h o t t , P a t r i c k H., 1980, " R e a l U s e r C o s t s and t h e Demand f o r S i n g l e - F a m i l y H o u s i n g " , B r o o k i n g s P a p e r s on E c o n o m i c A c t i v i t y . H eung, Raymond, 1976, The Do's and D o n ' t s o f H o u s i n g P o l i c y : The C a se o f B r i t i s h C o l u m b i a , V a n c o u v e r : The F r a s e r I n s t i t u t e . H i r s h , A l b e r t A. & M i c h a e l C. L o v e l l , 1969, S a l e s A n t i c i p a t i o n s a nd I n v e n t o r y B e h a v i o u r , New Y o r k : W i l e y . J a f f a r y , K a r l , M i c h a e l A u d a i n , L a r r y B e l l , J o h n B r e w i n , B r u c e M c C u l l o c h , M i n i s t r y o f H o u s i n g - I n t e r d e p a r t m e n t a l S t u d y Team on H o u s i n g and R e n t s , 1975, H o u s i n g & R e n t C o n t r o l i n B r i t i s h C o l u m b i a ( O c t o b e r ) . J a f f e e , D w i g h t M. & K e n n e t h T. R o s e n , 1979, " M o r t g a g e C r e d i t A v a i l a b i l i t y a n d R e s i d e n t i a l C o n s t r u c t i o n " , , B r o o k i n g s P a p e r s on E c o n o m i c A c t i v i t y , V o l 2. pp 3 3 3 - 3 7 6 . J o n e s , L a w r e n c e D, 1983, "The S t a t e o f t h e R e n t a l M a r k e t : I m p l i c a t i o n s f o r CMHC a n d F e d e r a l G o v e r n m e n t H o u s i n g P o l i c y i n t h e 1 9 8 0 ' s " , P r e p a r e d f o r C anada M o r t g a g e a n d H o u s i n g C o r p o r a t i o n , ( M a y ) . K e a r l , J.R., 1979, " I n f l a t i o n , M o r t g a g e s a n d H o u s i n g " , 123 ' J o u r n a l o f P o l i t i c a l Economy, V o l 87, No 5. L o v e l l , M i c h a e l , 1961, " M a n u f a c t u r e r s ' I n v e n t o r i e s , S a l e s E x p e c t a t i o n s , a n d t h e A c c e l e r a t i o n P r i n c i p l e " , E c o n o m e t r i c a V o l 29, No 3 ( J u l y ) , pp 293-314. M a d d a l a , G.S., 1977, E c o n o m e t r i c s , New Y o r k : M c G r a w - H i l l Book Company. M a i s e l , S . J . , 1963, "A T h e o r y o f F l u c t u a t i o n s i n R e s i d e n t i a l C o n s t r u c t i o n S t a r t s " , The A m e r i c a n E c o n o m i c R e v i e w , V o l 53 ( J u n e ) p p 359-379. Mason, J o h n M., 1979, "The S u p p l y C u r v e f o r H o u s i n g " , AREUEA J o u r n a l , V o l 7, pp 362-377. M e l t z e r , L l o y d A., 1940, "The N a t u r e a n d S t a b i l i t y o f I n v e n t o r y C y c l e s " , The R e v i e w o f E c o n o m i c S t a t i s t i c s V o l 22, No 4 ( N o v ) , p p 1 1 3 - 1 2 9 . M u t h , J o h n F., 1961, " R a t i o n a l E x p e c t a t i o n s a n d t h e T h e o r y o f P r i c e M ovements", E c o n o m e t r i c a , V o l 29, No 3 ( J u l y ) pp 315-335. Q u i g l e y , J o h n M., 1978, " H o u s i n g M a r k e t s and H o u s i n g Demand: A n a l y t i c a l A p p r o a c h e s " , i n L a r r y S. B o u r n e & J o h n R. H i t c h c o c k ( e d ) , U r b a n H o u s i n g M a r k e t s : R e c e n t D i r e c t i o n s i n R e s e a r c h and P o l i c y . R o s e n , K e n n e t h T., 1979, "A R e g i o n a l M o d e l o f M u l t i f a m i l y H o u s i n g S t a r t s " , AREUEA J o u r n a l , V o l 7 ( S p r i n g ) . R o s e n , K e n n e t h T. & L a w r e n c e B. S m i t h , 1982, "The P r i c e A d j u s t m e n t P r o c e s s f o r R e n t a l H o u s i n g a n d t h e N a t u r a l V a c a n c y R a t e " , C e n t e r f o r R e a l E s t a t e a n d U r b a n E c o n o m i c s , U n i v e r s i t y o f C a l i f o r n i a , B e r k l e y , WP 82 - 5 3 . R y d e l l , C. P e t e r , 1981, " P r i c e E l a s t i c i t i e s o f H o u s i n g S u p p l y " , U.S. D e p a r t m e n t o f H o u s i n g and U r b a n D e v e l o p m e n t , W o r k i n g P a p e r WD-930-HUD ( F e b r u a r y ) . S m i t h , L a w r e n c e B., 1969, "A B i - S e c t o r a l H o u s i n g M a r k e t M o d e l " , The C a n a d i a n J o u r n a l o f E c o n o m i c s , V o l I I , no 4 ( N o v e m b e r ) , pp 55 7 - 5 6 9 . S m i t h , L a w r e n c e B., 1974, The P o s t w a r C a n a d i a n H o u s i n g a n d R e s i d e n t i a l M o r t g a g e M a r k e t s a n d t h e R o l e o f G o v e r n m e n t , T o r o n t o : U n i v e r s i t y o f T o r o n t o P r e s s . S m i t h , L a w r e n c e B., 1974, "A N o t e on t h e P r i c e A d j u s t m e n t M e c h a n i s m f o r R e n t a l H o u s i n g " , The A m e r i c a n E c o n o m i c R e v i e w , V o l 64, No 3 ( J u n e ) pp 4 7 8 - 4 8 1 . S m i t h , L a w r e n c e B., 1977, Anatomy o f a C r i s i s : C a n a d i a n 124 H o u s i n g P o l i c y i n t h e S e v e n t i e s , V a n c o u v e r : The F r a s e r I n s t i t u t e . S m i t h , L a w r e n c e B., 1981, C a n a d i a n H o u s i n g P o l i c y i n t h e S e v e n t i e s " , L a n d E c o n o m i c s , V o l 57, No 3 ( A u g ) . S m i t h , L a w r e n c e B., 1982, "The C r i s i s . i n R e n t a l H o u s i n g : A C a n a d i a n P e r s p e c t i v e " , C e n t e r f o r R e a l E s t a t e a n d U r b a n E c o n o m i c s , U n i v e r s i t y o f C a l i f o r n i a , B e r k l e y , WP 8 2 - 4 9 . S m i t h , L a w r e n c e B, & P e t e r T o m l i n s o n , 1981, "Rent C o n t r o l s i n O n t a r i o : R o o f s o r C e i l i n g s ? " , AREUEA J o u r n a l . V o l 9, pp 93-114. S t e e l e , M a r i o n , 1979, The Demand f o r H o u s i n g i n C a n a d a , O t t a w a : S t a t i s t i c s C a n a d a . S t e v e n s , N e i l A., 1976, " H o u s i n g : A C y c l i c a l I n d u s t r y on t h e U p s w i n g " , F e d e r a l R e s e r v e Bank o f S t . L o u i s ( A u g ) . Swan, C r a i g , 1973, " H o u s i n g S u b s i d i e s a n d H o u s i n g S t a r t s " , AREUEA V o l 1, No 2 ( F a l l ) . T h e i l , H e n r i , 1966, A p p l i e d E c o n o m i c F o r e c a s t i n g , C h i c a g o : Rand M c N a l l y & Company. W a l k e r , M.A., e t a l , 1975, Rent C o n t r o l : A P o p u l a r P a r a d o x : E v i d e n c e o f t h e E c o n o m i c E f f e c t o f R e n t C o n t r o l , V a n c o u v e r The F r a s e r I n s t i t u t e . W a s l a n d e r , H.E.L., 1973, CANDIDE MODEL 1.0: R e s i d e n t i a l C o n s t r u c t i o n , O t t a w a : E c o n o m i c C o u n c i l o f C a n a d a . W e i c h e r , J . C . , 1976, "The R a t i o n a l e f o r Gov e r n m e n t I n t e r v e n t i o n i n H o u s i n g : An O v e r v i e w " , i n H o u s i n g i n t h e S e v e n t i e s : W o r k i n g P a p e r s , W a s h i n g t o n D . C : U.S. D e p a r t m e n t o f H o u s i n g a n d U r b a n D e v e l o p m e n t . W e i c h e r , J o h n C , e t a l , 1981, R e n t a l H o u s i n g : I s T h e r e a C r i s i s ? , W a s h i n g t o n D . C : The U r b a n I n s t i t u t e P r e s s . W i c k s , Anne P a t r i c i a , 1982, "An A n a l y s i s o f t h e E f f e c t s o f MURB L e g i s l a t i o n on V a n c o u v e r ' s R e n t a l H o u s i n g M a r k e t " , u n p u b l i s h e d MSc T h e s i s - UBC ULE D i v i s i o n . ( A p r i l ) 1 25 APPENDIX A E s t i m a t i o n o f R e n t a l H o u s e h o l d A. To e s t i m a t e t h e number o f e x p e c t e d new r e n t a l h o u s e h o l d s p e r q u a r t e r , b a s e d on d e m o g r a p h i c demand, t h e f o l l o w i n g a s s u m p t i o n s were made: 1. The h e a d s h i p r a t e s and p e r c e n t a g e o f a p a r t m e n t d w e l l e r s f o r e a c h age c o h o r t w i l l be s e t a t t h e 1971 r a t e s . 2. The g r o w t h i n t h e number o f h o u s e h o l d s i s l i n e a r . T h e r e f o r e , t h e r a t e o f cha n g e o r number o f new h o u s e h o l d s p e r q u a r t e r w i l l be c o n s t a n t . 3. A d j u s t m e n t s t o t h e ba s e p o p u l a t i o n a r e made p e r q u a r t e r b a s e d on t h e s u r v i v o r s h i p r a t e s p e r c o h o r t . No a d j u s t m e n t i s made f o r b i r t h s s i n c e t h e s e w i l l n o t a f f e c t t h e c o h o r t s l i k e l y t o become a h o u s e h o l d h e a d . 4. A t e a c h c e n s u s , t h e t o t a l p o p u l a t i o n i s a d j u s t e d t o a c c o u n t f o r g r o w t h f r o m m i g r a t i o n . 126 B. The f o l l o w i n g s t e p s were t a k e n t o c a l c u l a t e t h e e x p e c t e d new r e n t a l h o u s e h o l d s : . 1 . The p o p u l a t i o n p e r c o h o r t (by s e x ) was m u l t i p l i e d by a q u a r t e r l y s u r v i v o r s h i p r a t e . 2. The p o p u l a t i o n f r o m ( 1) was m u l t i p l i e d by t h e h e a d s h i p r a t e p e r c o h o r t t o y i e l d t h e t o t a l h o u s e h o l d s e x p e c t e d . 3. The number of h o u s e h o l d s f r o m (2) was m u l t i p l i e d by t h e p e r c e n t a g e o f a p a r t m e n t d w e l l e r s t o e s t i m a t e t h e t o t a l r e n t a l h o u s e h o l d s . 4. The q u a r t e r l y c h a n g e f o r t h e r e s u l t s i n (3) were u s e d as t h e v a r i a b l e 'DEAPT', o r e x p e c t e d new r e n t a l h o u s e h o l d s f r o m d e m o g r a p h i c demand. 1 27 C. The f o l l o w i n g data represent the population, headship rates and percentages of apartment households for 1971. These are the base for the above c a l c u l a t i o n s . AGE POPULATION HOUSEHOLDS HEADSHIP RATE COHORT MALE FEMALE MALE FEMALE MALE FEMAL1 <1 5 132155 126255 1 5-24 89635 91515 18175 6770 .2028 .0740 25-34 73450 71 260 60720 9115 .8267 . 1 279 35-44 644 1 0 601 55 60420 7465 . 9381 .1241 45-54 58590 62730 55275 1 0650 . 9434 . 1 698 55-64 45790 48940 42350 1 2490 . 9249 .2552 65-69 1 5840 17 140 1 3855 6360 .8747 .3710 70 + 29695 40820 23430 1 8800 .7890 . 4606 AGE COHORT HOUSEHOLDS MALE FEMALE APARTMENTS MALE FEMALE % APARTMENT MALE FEMALE 1 5-24 181 75 6770 1 1 605 5775 63. 85 85.30 25-34 60720 9115 21445 6535 35. 32 71.70 35-44 60420 7465 971 5 3875 16. 08 51 .91 45-54 55275 1 0650 9135 5295 16. 52 49.72 55-64 42350 12490 9095 6220 21 . 48 49.80 65-69 1 3855 6360 3685 3260 26. 60 51 .26 70 + 23430 18800 7505 1 0530 32. 03 56.01 1 28 APPENDIX B DATA SERIES YEAR QTR ABSORB BCFAMALN DEAPT WAC APTSTK 1 963 1 -754 78.75 4.20 83680 1 963 2 766 1 55 78.75 4.20 85317 1963 3 707 695 78.88 4.20 86955 1 963 4 1161 922 78.88 4. 20 88593 1 964 1 1 1 30 425 78.88 4. 30 90324 1 964 2 .1143 573 7 8 . 8 1 4.45 921 08 1 964 3 528 937 78.94 4.60 93897 1964 4 1 521 1 1 39 78.88 4.70 95642 1965 1 1 740 674 78.81 4.50 97085 1 965 2 2278 602 78.88 4.30 98521 1 965 3 1 965 1 664 78.88 4.10 99952 1 965 4 184 1 1999 78.81 4.00 101482 1966 1 2333 91 1 224.19 3. 50 102582 1 966 2 2089 924 224.19 3.00 103671 1 966 3 1 778 2058 224.06 2.00 104741 1 966 4 1 577 1854 224.19 . 1 .50 106326 1 967 .1 1 249 392 224 . 1 3 1 . 40 108333 1 967 2 1 237 201 224. 19 1 . 30 110335 1 967 3 1 827 • 1 165 224. 19 1 .20 112334 1 967 4 1 655 1 405 224.13 1 .00 114213 1 968 1 2044 212 224.19 1.10 116437 1 968 2 2033 207 224.13 1 .20 118665 1 968 3 1 728 989 224.13 1 .25 120836 1968 4 2337 1 425 224. 19 1 . 30 123009 1 969 1 1 591 414 224. 13 1 .28 125096 1 969 2 1 848 554 224.13 1 .26 127182 1 969 3 2242 1 056 224.25 1 .24 129268 1969 4 2632 2071 224.00 1 .20 131326 1 970 1 2579 519 224.25 2.00 134526 1 970 2 2078 931 224.06 2.70 137636 1 970 3 2255 1 030 224.19 2.40 139349 1970 4 2003 1068 224. 19 2.10 141052 1 971 1 1 746 492 520.35 3.10 144659 1 971 2 2270 285 520.50 4.10 148342 1 971 3 1 994 1 374 520.44 3.50 148620 1 971 4 2434 1 773 520.38 2.80 148742 1 972 1 1 972 . 814 520.38 2.60 149625 1 972 2 1 1 38 438 520.31 2.40 150506 1 972 3 1411 1 077 520.56 1 .50 150307 1 972 4 1 557 1608 520.38 .60 150112 1 973 1 1 741 785 520.38 .80 151583 1973 2 1 276 844 520.50 1 .00 153059 1 973 3 862 1 465 520.38 .60 153608 1 29 YEAR QTR ABSORB BCFAMALN DEAPT WAC APTSTK 1 9 7 3 4 1 8 6 4 1 8 0 4 5 2 0 . 3 8 . 4 0 1 5 4 4 6 3 1974 1 1 7 74 8 6 2 5 2 0 . 3 8 . 4 0 1 5 5 6 2 6 1974 2 1 618 9 8 7 5 2 0 . 3 1 . 3 0 1 5 6 6 3 2 1 9 7 4 3 8 7 2 9 54 5 2 0 . 5 0 . 2 0 1 5 7 6 3 6 1 9 7 4 4 1 4 7 8 1 1 72 5 2 0 . 3 8 . 1 0 1 5 8 6 3 8 1 9 7 5 1 1 8 5 6 1 23 5 2 0 . 5 6 . 1 0 1 5 9 7 9 7 1 9 7 5 2 1 6 3 2 - 2 6 9 5 2 0 . 4 4 . 2 0 1 6 1 1 1 8 1 9 7 5 3 1 6 0 9 - 1 2 4 5 2 0 . 2 5 . 2 0 1 6 2 2 8 0 1 9 7 5 4 2 2 8 0 2 4 0 5 2 0 . 5 0 . 10 1 6 3 2 7 6 1 9 7 6 1 8 1 3 - 3 5 1 5 0 8 . 7 2 . 2 0 1 6 4 6 0 1 1 9 7 6 2 1 1 97 1 78 5 0 8 . 9 4 . 4 0 1 6 6 0 9 4 1 9 7 6 3 1 5 4 6 - 6 4 5 0 8 . 6 3 . 5 0 1 6 7 8 9 3 1 9 7 6 4 1 2 9 5 92 5 0 8 . 7 5 . 7 0 1 6 9 8 6 7 1 9 7 7 1 1 5 8 7 140 5 0 8 . 7 5 1 . 1 0 1 7 2 1 9 5 1 9 7 7 2 1 1 1 5 189 5 0 8 . 6 9 1 . 6 0 1 7 4 7 2 1 1 9 7 7 3 1 0 3 0 561 5 0 8 . 8 1 1 . 6 0 1 7 6 3 7 1 1 9 7 7 4 2 3 2 7 9 5 8 5 0 8 . 7 5 1 . 6 0 1 7 8 0 2 1 1 9 7 8 1 1 6 4 7 3 1 2 5 0 8 . 5 6 1 . 5 0 1 7 9 4 8 8 1 9 7 8 2 2 601 51 1 5 0 8 . 7 5 1 . 50 1 8 1 1 3 7 1 9 7 8 3 2 3 6 4 9 9 0 5 0 8 . 6 9 1 . 40 1 8 2 6 0 0 1 978 4 7 8 6 9 4 5 5 0 8 . 6 3 1 . 4 0 1 8 4 2 4 7 1 9 7 9 1 6 9 3 3 9 7 5 0 9 . 0 0 1 . 2 0 1 8 5 5 1 7 1 9 7 9 2 861 5 5 6 5 0 8 . 5 6 . 9 0 1 8 6 5 9 4 1 9 7 9 3 1 1 29 1 8 5 2 5 0 8 . 8 1 . 6 0 1 8 7 6 6 5 1 9 7 9 4 5 6 8 1 9 4 8 5 0 8 . 6 3 . 2 0 1 8 8 5 4 0 1 9 8 0 1 7 5 5 1 2 8 7 5 0 8 . 8 8 . 10 1 8 9 9 7 6 1 9 8 0 2 6 6 7 9 9 5 5 0 8 . 8 1 . 10 1 9 1 6 0 2 1 9 8 0 3 1 2 4 8 1 5 0 4 5 0 8 . 6 3 . 1 0 1 9 3 2 2 7 1 9 8 0 4 1 0 0 2 21 52 5 0 8 . 8 1 . 1 0 1 9 4 8 5 3 1981 1 1 0 1 3 9 1 7 . 1 0 1 9 6 4 7 7 1981 2 7 0 6 7 7 6 . r o 1 9 8 1 0 3 1 981 3 1 0 6 5 3 1 5 . 1 0 1 9 9 7 2 9 1981 4 9 4 3 7 1 3 . 1 0 2 0 1 3 5 3 1 9 8 2 1 1 1 65 - 5 2 7 . 1 0 2 0 2 9 7 9 1 9 8 2 2 1 521 - 7 9 . 60 2 0 5 6 3 4 1 9 8 2 3 2 1 4 4 - 1 0 3 . 9 0 2 0 7 8 9 5 1 9 8 2 4 - 2 9 1 . 9 0 2 1 1 6 6 9 MEAN 5 5 2 . 1 4 7 7 8 . 2 0 3 2 4 . 2 5 4 1 . 6 4 2 1 4 7 9 7 6 . 8 8 MIN 5 2 8 - 7 5 4 . 1 0 8 3 6 8 0 MAX 2 6 3 2 21 52 5 2 0 . 5 6 4 . 7 0 21 1 6 6 9 STDEV 5 5 8 . 15 6 4 6 . 8 2 2 0 3 . 1 9 7 1 . 4 4 5 3 6 2 6 7 . 7 1 VARIANCE 1 5 3 4 . 8 4 1 8 3 7 1 . 0 4 1 2 8 9 . 0 2 . 0 8 9 ********* YEAR QTR BCUR RINC CPI 1 963 1 0.0 6.45 80.10 1 963 2 0.0 6.44 80.20 1 963 3 0.0 6.42 80.40 1 963 4 0.0 6.43 80.30 1 964 1 0.0 6.81 80.40 1 964 2 0.0 6.78 80.70 1 964 3 0.0 6.76 81 .00 1 964 4 0.0 6.73 81 .40 1 965 1 0.0 7.25 82.00 1 965 2 0.0 7.26 81 .80 1 965 3 0.0 7.19 82.60 1 965 4 0.0 7. 16 83.00 1 966 1 4.90 7.66 83.90 1 966 2 4.40 7.65 84. 00 1 966 3 4.40 7.57 84.90 1 966 4 5.20 7.55 85.10 1 967 1 5. 40 8.00 85.90 1 967 2 4.90 7.88 87.30 1 967 3 3. 90 7.79 88. 30 1 967 4 5.60 7.70 89.30 1 968 1 6.30 8.10 89.90 1 968 2 6.30 8.08 90.20 1 968 3 5.10 7.98 91.30 1 968 4 5. 10 7.92 92.00 1 969 . 1 5.30 8.71 92.60 1 969 2 4.30 8. 54 94 . 40 1 969 ' 3 4 . 40 8.57 94. 1 0 1 969 4 5.20 8.46 95. 30 1 970 1 6.60 8.88 95.90 1 970 2 9.60 8.73 97. 50 1 970 3 7.20 8.76 97.20 1 970 4 7.40 8.71 97.70 1 971 1 8.20 9.51 98.50 1 971 2 7.40 9.39 99.70 1 97 1 3 6.20 9.28 100.90 1 971 4 6.60 9.12 102.70 1 97 2 1 8.70 10.11 103.90 1 972 2 8.10 10.01 104.90 1 972 3 7.40 9.89 106.20 1 972 4 8.10 9.77 107.50 1 973 1 7.50 11.21 109.80 1 973 2 6. 50 10.95 112.40 1 973 3 6.00 1 0 .64 115.60 YEAR QTR BCUR RINC CPl 1 97 3 4 5.80 10.50 1 17.20 1 974 1 5.80 1 1 .93 120.70 1 974 2 5.50 11.43 126.00 1 974 3 6.10 11.10 129.70 1 974 4 6.80 10.77 133.70 1 975 1 9.20 12.02 135.00 1 975 2 7.80 1 1 .64 139.40 1 975 3 8.80 1 1 .28 143.80 1 975 4 7.50 11.16 145.40 1976 1 9.10 12.27 150.20 1 976 2 8.10 1 1 .95 154.20 1 976 3 7.70 11.74 157.00 1 976 4 8.20 1 1 . 66 158.00 1 977 1 9.30 1 2.65 161.30 1 977 2 7.80 12.42 164.20 1977 3 7.50 12.23 166.80 1 977 4 8.00 1 1 .98 170.20 1978 1 9.10 12.96 173.50 1978 2 7.20 12.65 177.70 1 978 3 7.30 12.48 180.20 1978 4 8.50 12.28 183.00 1 979 1 8.60 1 3.24 187.50 1 979 2 7.00 12.98 191.20 1 979 3 6.80 12.76 194.50 1 979 4 7.10 12.60 197.00 1 980 1 8.40 1 3. 67 201.60 1980 2 6.10 13.22 208.50 1 980 3 5.90 12 . 9 1 213.60 1 980 4 6.10 12.50 220.50 1 981 1 6.80 13.56 231.20 1981 2 5.50 13.15 238.30 1 981 3 7.00 12.79 24 5.10 1981 4 8.60 12.47 251.40 1 982 1 10.60 0.0 257.60 1 982 2 1 1 .50 0.0 264.40 1 982 3 12.80 0.0 268.70 1 982 4 1 4 .80 0.0 270.50 MEAN 6.0862 9.4968 134.770 MIN 0.0 0.0 80.10 MAX 14.80 13.67 270.50 STDEV 3.1466 3.1216 56.0409 VARIANCE 9.9012 9.744182 3140.58 YEAR QTR RRENT 1 963 1 102.37 1 963 2 102.37 1963 3 102.24 1 963 4 102.37 1 964 1 102.24 1 964 2 102.48 1 964 3 102.22 1 964 4 101.72 1 965 1 100.98 1 965 2 101.71 1 965 3 100.97 1 965 4 100.72 1 966 1 99.88 1 966 2 100.60 1 966 3 100.12 1 966 4 100.71 1 967 1 100.23 1 967 2 100.11 1 967 3 100.00 1 967 4 100.00 1 968 1 100.00 1 968 2 101.22 1 968 3 100.99 1968 4 101.20 1969 1 101.08 1969 2 100.64 1969 3 101.91 1 969 4 101.57 1 970 1 101.56 1 970 2 100.62 1970 3 101.65 1 970 4 101.54 1 97 1 1 101.02 1971 2 100.30 1971 3 99.4 1 1 97 1 4 97.96 1 972 1 97. 1 1 1972 2 96.57 1 972 3 95.86 1972 4 95. 1 6 1 973 1 93.53 1 973 2 92.53 1 973 3 91 .09 RENTMTG RENTRMTG 1462. 46 1 481 . 46 1503 .22 1460. 55 1503 .51 1462. 37 1 441 .78 1460. 55 1481 .72 1489. 51 1 557 .42 1460. 32 1525 .71 1 453. 1 4 1 541 .21 1480. 58 1 623 .40 1 489. 1 9 1 446 .82 1412. 1 5 1 590 . 06 1361. 1 2 1 438 .90 1 338. 88 1 522 .57 1328. 87 1 346 .66 1 277 . 01 1 442 .62 1 266. 73 1 299 .42 1280. 1 1 1425 .79 1 270. 49 1 544 .98 1234 . 57 1408 .45 1 1 73. 71 1 329 .79 1116. 07 1 196 . 1 7 1 1 02. 61 1 1 39 .86 1118. 34 . 1 273 .46 1112. 04 1204 .71 1 066. 24 1 138 .29 1038. 55 1 275 .48 1008. 04 978 .99 967. 37 1092 . 1 9 959. 96 1017 .68 955. 51 1 126 .71 981 . 1 4 953 .53 999. 36 1 051 .09 1088. 53 1 191 .22 1 073. 89 1 232 .20 1040. 89 1 190 .48 1 076. 43 1 341 .85 1 082. 64 1 249 .84 1030. 61 1 153 .74 1021 . 93 1 186 .35 1032. 1 3 1 201 .55 1031 . 24 1 381 . 59 971 . 92 1337 .09 899. 21 1314 .43 YEAR QTR RRENT RENTMTG RENTRMTG 1 973 4 • 90.61 904.33 1076.18 1 974 1 88.98 886.26 1360.56 1 974 2 86.59 761.54 1426.48 1 974 3 85.51 709.58 1024.01 1 974 4 84.07 707.65 1066.86 1 975 1 84.44 792.91 903.15 1 975 2 83.50 743.55 1222.56 1 975 3 82.68 692.50 1096.61 1 975 4 83.08 698.75 807.40 1 976 1 82.02 689.28 1155.27 1 976 2 81.06 679.49 1022.24 1 976 3 81.15 690.02 905.65 1 976 4 8 1 .84 726.14 796.84 1 977 1 81.77 797.79 1 176.59 1 977 2 81.12 783.77 1088.87 1 977 3 80.88 783.68 1047.61 1 977 4 79.85 772.96 1152.20 1 978 1 78.85 763.28 1121.58 1 978 2 77.55 751.42 1267.10 1 978 3 77.25 723.97 945.50 1978 4 76.78 665.88 879.45 1979 1 75.52 679.75 1142.51 1 979 2 74.69 669.23 1001 . 1 5 1979 3 74.29 606.47 830.09 1 979 4 74.21 546.49 669.79 1 980 1 73.26 498.73 726. 10 1 980 2 71 .56 553.86 1188.69 1 980 3 71.11 490.44 756.53 1 980 4 70.43 451.48 809.55 1 981 . 1 68.56 435.27 1357.53 1 981 2 68.02 366.70 594.09 1981 3 67.93 316.55 463.38 1 9 8 1 4 68.02 382.34 591.99 1 982 1 67.97 350.20 514.56 1 982 2 68.08 1 982 3 68.74 1 982 4 69.43 MEAN 89.4990 954.4249 1163.042 MIN 67.93 316.55 463.38 MAX 102.48 1489.51 1623.40 STDEV 12.3737 325.2779 269.2333 VARIANCE 153.1 1 0 105805.7 72486.56 YEAR QTR VMFST VMFINV VMFUC ABSPRED 1 963 1 971 254 2255 1 963 2 820 428 2037 793 1 963 3 1 231 429 2566 . 820 1 963 4 2045 589 3269 1 038 1964 1 1592 48 1 3801 1228 1964 2 1 984 478 4662 1121 1964 3 2928 609 6864 998 1 964 4 1 992 1686 5959 1 254 1965 1 1 1 64 1918 4981 2005 1 965 2 3108 1014 6720 2124 1965 3 1 884 1 351 6232 1 484 1 965 • 4 1 430 761 6269 1914 1966 1 1 220 664 5056 1 902 1 966 2 920 762 3835 1883 1966 3 .1 349 608 3365 1 927 1 966 4 1 184 508 3085 1927 1967 1 ' 1 1 28 323 3116 1773 1967 2 1 678 414 3454 1618 1 967 3 2756 415 4085 1 791 1 967 4 1 798 359 4567 1 793 1968 1 1 932 442 41 34 1670 1 968 2 2735 257 5009 1 739 1 968 3 2051 220 5288 1722 1 968 4 3003 406 5758 1 958 1 969 1 3031 368 7231 2075 1 969 2 3445 328 8680 21 05 1 969 3 3627 484 981 7 2076 1 969 4 1 842 667 8864 2382 1970 1 2020 945 8027 2272 1 97 0 2 634 629 6746 1 9 9 8 1 970 3 1 899 953 591 0 2035 1 970 4 3213 346 7678 2404 1971 1 2261 662 7826 1711 1971 2 1875 964 6753 1877 1971 3 2099 1 074 6596 21 80 1 971 4 2587 659 7045 2330 1 972 1 1288 435 6792 1 754 1972 2 1 493 61 1 6970 1515 1 972 3 1 779 470 7323 1 602 1972 4 2336 449 8112 1619 1973 1 959 354 7302 1614 1973 2 1686 606 7375 1 541 1973 3 1 674 491 8262 1601 YEAR QTR VMFST VMFINV VMFUC ABSPRED 1 973 4 2963 285 9325 1737 1 974 1 1 1 28 340 8321 1517 1 974 2 2181 375 8682 1 371 1 974 3 1 525 695 8972 1 077 1 974 4 1515 919 8590 1 301 1 975 1 700 1 263 6805 1 170 1 975 2 855. 1690 5566 1 375 1 975 3 1 727 1417 5957 1 329 1 975 4 1 587 1 700 4898 1 564 1 976 1 1015 1 539 5231 1 556 1 976 2 1 507 1 399 5358 1510 1 976 3 1210 1 699 4210 1 279 1 976 4 2372 1699 5295 1655 1 977 1 1435 1 578 5030 1682 1 977 2 1903 1993 5049 1 688 1 977 3 1612 2289 5114 1882 1 977 4 2132 1 624 5270 21 76 1 978 1 2206 1641 5579 1608 1 978 2 290 1 246 3581 1 733 1 978 3 373 801 1 951 1 357 1978 4 686 637 2000 1 051 1 979 1 1115 575 2445 935 1 979 2 632 782 1 938 994 1 979 3 1013 477 2058 1 1 58 1 979 4 765 222 2504 1 1 04 1 980 1 1 574 253 3251 775 1 980 2 626 252 32 1 1 863 1 980 3 1 334 458 3042 777 1 980 4 1 901 418 4068 1110 1 9 8 1 1 1 772 232 501 7 1 9 8 1 2 1 748 432 5800 1 981 3 2400 870 6634 1 981 4 2080 ' 1638 6946 1 982 1 2376 2161 7407 1 982 2 1 630 2783 671 4 1 982 3 734 2807 1982 4 2 1 3 2691 MEAN 1693 . 6 884.39 5532.0 2531.3 MIN 2 1 3 220 1 938 775 MAX 3627 2807 981 7 9 9 9 9 STDEV 753.19 649.22 2055.5 2704.8 VARIANCE 567300 42 1486 ****** ****** YEAR QTR PROFIT RENT CC BKRAT 1 963 1 1 .02 82.00 69.90 4.00 1 963 2 1 .02 82. 10 72.70 3.50 1 963 3 1 .02 82.20 73.60 4.00 1 963 4 1 .02 82. 20 74.20 4.00 1 964 1 1 .02 82.20 74.90 4.00 1964 2 1 .02 82.70 77.80 4.00 1964 3 1 .02 82.80 77.70 4.00 1 964 4 1 .02 82.80 78. 10 4.25 1 965 1 1 .01 82.80 79.70 4.25 1965 2 1 .02 83.20 79.80 4.25 1 965 3 "1.01 83.40 80. 10 4.25 1 965 4 1.01 83.60 80.40 4.75 1 966 1 1 .00 83.80 81 .20 5.25 1 966 2 1.01 84.50 81 .90 5.25 1 966 3 1 .00 85.00 84.20 5.25 1 966 4 1.01 85.70 84.20 5.25 1 967 1 1 .00 86. 1 0 84.50 5.00 1 967 2 1 .00 87.40 85. 1 0 4. 50 1 967 3 1 .00 88.30 86.10 5.00 1 967 4 1 .00 89. 30 87.10 6.00 1 968 1 1 .00 89.90 88.80 7.50 1 968 2 1.01 91 . 30 90.40 7.50 1 968 3 1.01 92.20 9 1.70 6.00 1 968 4 1.01 93. 10 92.90 6.50 1 969 1 1.01 93.60 98.60 7.00 1 969 2 1.01 95. 00 98.00 7.50 1 969 3 1 .02 95.90 95.60 8.00 1 969 4 1 .02 96.80 95.20 8.00 1 970 1 1 .02 97.40 95.40 8.00 1 970 2 1.01 98. 10 94.60 7.00 1 970 3 1 .02 98.80 95.50 6.50 1 970 4 1 .02 99.20 95.40 6.00 1 971 1 1 .01 99. 50 96.60 5.25 1 971 2 1 .00 100.00 99.60 5.25 1 971 3 .99 100.30 102.00 5.25 1971 4 .98 100.60 103.90 4.7 5 1 972 1 .97 100.90 105.60 4.75 1 972 2 .97 101.30 108.20 4.75 1 972 3 .96 101.80 110.90 4.75 1 972 4 .95 102.30 114.80 4.75 1 973 1 .94 102.70 119.60 4.75 1 973 2 .93 104.00 121.20 6.25 1 973 3 .91 105.30 122.50 7.25 YEAR QTR PROFIT RENT CC BKRAT 1 973 4 .91 106.20 125.90 7.25 1 974 1 .89 107.40 130.20 7.25 1 974 2 .87 109. 10 132.30 8.75 1 974 3 .86 110.90 134.60 9.25 1974 4 .84 112.40 131.40 8.75 1 975 1 .84 114.00 134.50 8.25 1 975 2 .84 116.40 142.70 8.25 1 975 3 .83 1.18.90 146.50 9.00 1 975 4 .83 120.80 149.20 9.00 1 976 1 .82 123.20 153.90 9. 50 1 976 2 .81 125.00 155.40 9.50 1 976 3 .81 . 127.40 161.60 9.50 1 976 4 .82 129.30 165.50 8.50 1 977 1 .82 131.90 168.80 8.00 1 977 2 . . 8 1 133.20 174.80 7.50 1 977 3 .81 134.90 180.20 7. 50 1 977 4 .80 135.90 180.20 7.50 1 978 1 .79 136.80 186.40 8.00 1 978 2 .78 137.80 192.40 8.50 1 978 3 .77 139.20 195.70 9.50 1 978 4 .77 140.50 199.80 10.75 1 979 1 .76 141.60 208.10 1 1 .25 1 979 2 ,.75 142.80 212.00 11.25 1 979 3 .74 144.50 215.60 1 2.25 1 979 4 .74 146.20 209.40 14.00 1 980 1 .73 147.70 214.00 14.79 1 980 2 .72 149.20 219.80 10.67 1 980 3 .71 151.90 224 . 1 0 1 1 .02 1 980 4 .70 155.30 226.70 17.26 1 981 1 .69 158.50 234.20 1 6. 59 1 981 2 .68 162.10 250.20 19.07 1 981 3 .68 166.50 248.80 19.63 1 981 4 .68 171.00 248.00 14.66 1 982 1 .68 175.10 248. 10 15.11 1 982 2 .68 180.00 257.10 1 982 3 .69 184.70 258.70 1 982 4 .69 187.80 262.20 MEAN .8950 113.98 137.61 7.8123 MIN .68 82.00 69.90 3.50 MAX 1 .02 187.80 262.20 19.63 STDEV . 1 237 29.083 58.858 3.6694 VARIANCE .01 531 845.84 3464 . 2 13.465 1 38 APPENDIX C CORRELATION MATRIX ABSORB RRENT APTSTK1 DEAPT BCURD ABSORB 1 . 000 0. 382 -0. 181 -o. 138 -0. 186 RRENT 0. 382 1 . 000 -0. 899 -o. 751 0. 408 APTSTK1 -o. 181 -o. 899 1 . 000 0. 905 -0. 651 DEAPT -o. 1 38 -o. 751 0. 905 1 . 000 -o. 698 BCURD -o . 186 0. 408 -0. 651 -0. 698 1 . 000 QJ 0. 019 0. 01 1 -0. 002 0. 040 -0. 058 Q2 -o. 040 0. 014 -o. 029 -o. 013 0. 019 Q3 -o. 083 -0. 004 0. 003 -o. 013 0. 019 BCUR 0. 074 -0. 556 0. 789 0. 819 -0. 880 RCONTR -o. 313 -0. 933 0. 802 0. 674 -0. 346 BCFAMALN 0. 088 0. 074 -o. 034 -o. 1 02 0. 021 VMFINV1 0. 203 -0. 312 0. 255 0. 207 0. 034 WAC1 0. 1 1 7 0. 651 -o. 717 -o. 675 0. 757 GRANT 0. 1 1 4 -0. 1 90 0. 1 46 0. 216 -o. 1 05 AHOP 0. 020 -0. 551 0. 481 0. 449 -o. 231 RINC -o. 251 -0. 935 0. 973 0. 890 -o. 595 RENTMTG 0. 184 0. 887 -o. 960 - -o. 836 0. 689 RENTRMTG 0. 079 0. 669 -o. 776 -o. 610 0. 592 BCUR RCONTR BCFAMALN VMFINV1 WAC :1 ABSORB 0. 074 -0. 313 0. 088 0. 203 0. 1 1 7 RRENT -o. 556 -0. 933 0. 074 -0. 312 0. 651 APTSTK1 -o. 789 0. 802 -o . 034 0. 255 -o. 717 DEAPT 0. 819 0. 674 -o. 1 02 0. 207 -o. 675 BCURD -o. 880 -0. 346 0. 021 0. 034 0. 757 Q1 0. 169 0. 020 -o. 338 -o . 004 -o. 060 Q2 -o. 032 -0. 007 -o. 353 -o. 021 0. 024 Q3 -o. 105 -0. 007 0. 1 98 -o. 009 0. 059 BCUR 1. 000 0. 512 -o. 218 0. 212 -o. 719 RCONTR 0. 512 1 . 000 -o. 236 0. 415 -o. 631 BCFAMALN -o. 218 -o. 236 1. 000 -o. 331 0. 1 42 VMFINV1 0. 212 0. 415 -o. 331 1. 000 0. 017 WAC1 -o. 719 -o. 631 . 0. 142 0. 017 1. 000 GRANT 0. 223 0. 303 -o . 349 0. 246 -o. 279 AHOP 0. 467 0. 668 -o. 518 0. 760 -o. 372 RINC 0. 751 0. 868 -o . 141 0. 291 -o. 735 RENTMTG -o. 780 -0. 830 0. 048 -o. 187 0. 832 RENTRMTG -o. 680 -0. 61 1 -o. 026 -o . 1 1 1 0. 670 139 GRANT ABSORB 0. 1 1 4 RRENT -o. 190 APTSTK1 0. 1 46 DEAPT 0. 216 BCURD -o. 1 05 Q1 0. 006 Q2 -o. 002 Q3 -0. 002 BCUR 0. 223 RCONTR 0. 303 BCFAMALN -0. 349 VMFINV1 0. 246 WAC1 -0. 279 GRANT 1 . 000 AHOP 0. 453 RINC 0. 184 RENTMTG -o. 216 RENTRMTG -o. 1 99 QJ ABSORB 0. 019 RRENT 0. 01 1 APTSTK1 -o. 002 DEAPT 0. 040 BCURD -o. 058 Q1 1. 000 Q2 -o. 327 Q3 -o. 32 7 BCUR 0. 169 RCONTR 0. 020 BCFAMALN -o. 338 VMFINV1 -o. 004 WAC1 -o. 060 GRANT 0. 006 AHOP 0. 013 RINC 0. 106 RENTMTG 0. 024 RENTRMTG 0. 071 AHOP RINC 0.020 -0.251 -0.551 -0.935 0.481 0.973 0.449 0.890 -0.231 -0.595 0.013 0.106 -0.004 0.003 -0.004 -0.036 0.467 0.751 0.668 0.868 -0.518 -0.141 0.760 0.291 -0.372 -0.735 0.453 0.184 1 .000 • 0.544 0.544 1.000 -0.471 -0.938 -0.371 -0.704 Q2 Q3 -0.040 -0.083 0.014 -0.004 -0.029 0.003 -0.013 -0.013 0.019 0.019 -0.327 -0.327 1.000 -0.340 -0.340 1.000 -0.032 -0.105 -0.007 -0.007 -0.353 0.198 -0.021 -0.009 0.024 0.059 -0.002 -0.002 -0.004 -0.004 0.003 -0.036 0.043 -0.020 0.192 -0.076 RENTMTG RENTRMTG 0. 1 84 0.079 0.887 0.669 -0.960 -0.776 -0.836 -0.610 0.689 0.592 0. 024 0.071 0.043 0. 192 -0.020 -0.076 -0.780 -0.680 -0.830 -0.611 0.048 -0.026 -0.187 -0.111 0.832 0.670 -0.216 -0. 199 -0.471 -0.371 -0.938 -0.704 1 .000 0.840 0.840 1 .000 140 VMFST VMFST1 VMFINV1 ABSPRED VMFST 1 . 000 0. 420 - o . 1 1 4 0 . 457 Q2 - o . 105 - o . 1 65 -0. 021 -0. 068 Q3 0. 054 - o . 095 - o . 009 0. 072 Q4 0 . 1 95 0. 064 0 . 035 0 . 0 9 6 VMFST1 0. 420 1 . 000 - o . 1 18 0. 407 ABSPRED 0 . 457 0. 407 0. 276 1. 000 VMFUC1 0. 249 0. 560 0. 007 0. 455 BKRAT - o . 254 - o . 310 0. 044 - o . 406 PROFIT . 0. 372 0. 358 - o . 286 0. 410 WAC1 0. 129 0. 1 14 0. 017 0. 180 VMFINV1 - o . 1 1 4 - o . 1 18 1. 000 -0. 1 1 4 VMFUC1 BKRAT PROFIT WAC1 VMFST 0. 249 - o . 254 0. 372 0. 1 29 Q2 - o . 022 - o . 068 0 . 016 0 . 024 Q3 - o . 046 - o . 019 -0. 005 0. 059 Q4 - o . 015 0. 086 - o . 003 - o . 025 VMFST1 0. 560 - o . 310 0. 358 0. 1 1 4 ABSPRED 0. 455 - o . 406 0. 410 0. 180 VMFUC1 1 . 000 - o . 237 0. 1 77 - o . 096 BKRAT - o . 237 1 . 000 - o . 8 1 9 - o . 709 PROFIT 0. 177 - o . 819 1. 000 0. 702 WAC1 -0. 096 - o . 709 0. 702 1. 000 VMFINV1 - o . 02 1 - o . 009 0. 035 - o . 1 1 8 Q2 Q3 Q4 VMFST - o . 105 0. 054 0. 195 Q2 1. 000 - o . 340 - o . 340 Q3 -0. 340 1. 000 - o . 340 Q4 - o . 340 - o . 340 1. 000 VMFST1 - o . 1 65 - o . 095 0. 064 ABSPRED - o . 068 • 0 . 072 0. 096 VMFUC1 - o . 022 - o . 046 - o . 015 BKRAT -0. 068 - o . 019 0. 0 8 6 PROFIT 0. 016 - o . 005 -0. 003 WAC1 0. 0.2 4 0. 059 - o . 025 VMFINV1 - o . 021 - o . 009 0. 035

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