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800-5216600

THE NATURAL VACANCY RATE: AN ALTERNATIVE RENTAL APARTMENT MARKET INDICATOR

by

Adam Mark Szymczak

A Thesis Submitted to the College of Graduate Studies and Research

through the Department of Geography in Partial Fulfillrnent of the Requirements for

the Degree of Master of Arts at the University of Windsor

Wndsor, Ontario, Canada

0 1 998 Adam Mark Szymczak

National Libtary I*I of Canada Bibliothéque nationale du Canada

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L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

ABSTRACT

The balanced market vacancy r a t e i s a market i n d i c a t o r

u t i l i z e d by housing ana l ys t s t o determine one aspect o f t h e

p r i v a t e r e n t a l apartment market. The a c t o f comparing t h e

observed vacancy r a t e t o t he balanced r a t e supposedly revea l s t o

what degree a market i s over- o r under-suppl ied. However, t h e

balanced market vacancy r a t e i s assumed t o have t h e same va lue

f o r a17 c i t i e s , regard less o f market, demographic o r l e g i s l a t i v e

f a c t o r s . An a l t e r n a t i v e market i n d i c a t o r i s t h e na tu ra l vacancy

r a t e as def ined by Rosen and Smith (1983). The n a t u r a l vacancy

r a t e i s a r a t e a t wh'ch change i n r e a l r e n t s i s zero. I t i s

assumed t h a t f a c t o r s such as government r e g u l a t i o n s have, over

t ime, a f f e c t e d the market. Th is suggests t h a t t h e n a t u r a l vacancy

r a t e i s p re fe rab le t o t h e balanced market vacancy r a t e as a

market i n d i c a t o r because i t considers va r i ous socio-economic and

demographi c v a r i ab1 es.

A pooled data 1 i n e a r regress ion a n a l y s i s was used t o

eva iuate the usefu lness o f t h e n a t u r a l vacancy r a t e mode1 as a

market i ndi c a t o r . Addi t i onal 1 y, t h e components o r determi nants of

t h e n a t u r a l vacancy r a t e were examined us ing a m u l t i p l e

regress i on. Thi s s tudy found t h a t a f u n c t i onal r e l a t i o n s h i p

e x i s t e d between t h e percen t change i n r e n t and d i f f e r e n c e between

t h e observed vacancy r a t e and t h e n a t u r a l vacancy r a t e . The

r e l a t i o n s h i p between t h e components o f t h e n a t u r a l vacancy r a t e

and t h e l e v e l o f the n a t u r a l vacancy r a t e was uncer ta in . Though

t h e c o r r e l a t i o n c o e f f i c i e n t i ndicated a s t r o n g and d i r e c t

r e l a t i o n s h i p , cau t i on should be used i n i n t e r p r e t i n g the

regress ion s t a t i s t i c s s ince the sample s i r e w a s smal l .

iii

I would l i k e t o take t h i s oppor tun i ty t o extend m y g ra t i tude

t o D r . A . Vak i l , rny primary advisor , and Doug Caruso, my second

reader, f o r t h e i r feedback and guidance. 1 would a l so 1 i ke t o

o f f e r rny apprec ia t ion t o D r . P. Angl in, m y ex te rna l examiner, f o r

h i s val uable comments and feedback, espec ia l l y i n regards t o the

mode1 and t e s t i n g .

Speci a l thanks t o t he "are you done yet " crew who helped me

through t h i s ordeal ( i n no p a r t i c u l a r o rder ) : Bernadette Bruette,

Heather Jablonski , Jim Yanchula, Phi1 8 A l l i s o n Brand, C u r t i s

Keabl e, Brendan 8 D i anne Kennal ey, Chri s Matthews, Isabel Qui roz

de O1 ivares, Chr is & L isa Muggridge, John Pucher 8 Cindy Schultz,

Candi ce Sarnecki , James Stummer, Bev 8 Gerry Muggri dge, Pam

Wainwright & Steve W i l l i s , Lui Carvel lo, and Alex Gartenburg.

To the Scot t fami l y - Chri s, Pam, Chelsea, Megan and A l e x - w h o helped m e t o procras t ina te , provided me w i t h hours of

enjoyment, and most o f a l 1 , f o r t h e i r f r i endsh ip .

1 w i sh t o thank m y mother, Jadwiga. Without her support and

encouragement throughout these fou r years, none o f t h i s would be

possi b l e.

F i n a l l y , a huge thank you t o m y w i f e T ina f o r her patience,

understanding, guidance, and support, from beginning t o end.

Ja kocham c i ebie.

TABLE OF CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L I S T OF FIGURES

L I S T OF TABLES

L I S T OF ABBREVIATIONS

CHAPTER

1 INTRODUCTION

2 REVIEW OF THE LITERATURE 2.1 O v e r v i e w 2 . 2 S t u d i e s a n d R e s u l t s 2 . 3 Inferences and C r i t i q u e s 2 .4 Summary

3 A P R I O R I MODEL 3.1 P r i c e - A d j u s t m e n t M e c h a n i sm 3.2 R a t i o n a l e 3.3 L i m i t a t i o n s o f the Mode1 3.4 H y p o t h e s e s

4 METHODOLOGY 4 . 1 A r e a s of S t u d y 4 . 2 S a m p l i n g F r a m e 4 . 3 D a t a C o l l e c t i o n

5 RESULTS AND DISCUSSION 5.1 O v e r v i e w 5.2 H y p o t h e s i s One : P r i c e - A d j u s t m e n t M e c h a n i s m

5 .2 .1 Ind i v i dual R e g r e s s i ons 5 . 2 . 2 P o o l ed D a t a R e g r e s s i on

5.3 T h e N a t u r a l V a c a n c y R a t e 5 . 4 H y p o t h e s i s Two: D e t e r m i n a n t s o f t h e N a t u r a l

V a c a n c y R a t e 5 .5 D i scussi on

6 CONCLUSION 6.1 L i m i t a t i o n s 6 . 2 F u t u r e R e s e a r c h 6.3 Summary

REFERENCES

APPENDIX A: I n d i v i d u a l S t a t i s t i c a l R e p o r t s

APPENDIX B: P o o l e d D a t a S t a t i s t i ca l R e p o r t

APPENDIX C: N a t u r a l V a c a n c y S t a t i s t i c a l R e p o r t

V I T A AUCTORIS

L I S T OF FIGURES

FIGURE 1 : Rental P r i ce-Ad justment Mechani sm

FIGURE 2 : Areas of Study

LIST OF TABLES

TABLE 1 : Ind iv idua l Regressions Summary

TABLE 2 : Pooled Data Regression Summary

TABLE 3: Natura l Vacancy Rate Regression Summary

LIST OF ABBREVIAT f ONS

b l

b

be ta X

BMVR

CA

CMA

CMHC

cPOP

cSH

D

9

MOB

NVR, Vn

OVR, VR

PCR

RNT

R

R*

Rm

Rn

PS

S

S t a t C a n

U . S .

VL

Slope w i t h respect t o vacancies

Regressi on coe f f i c i en t

I n t e r c e p t as a f u n c t i o n o f independent v a r i a b l e s X

Balanced market vacancy r a t e

Census aggl omerati on

Census metropol i t a n area

Canada Mortgage and Housing Corporat ion

Average annual growth i n populat ion

Average annual change i n t o t a l housing s tock

Quanti t y o f r en ta l housi ng demanded

Rate of change

Renter m o b i l i t y r a t e

Natura l vacancy r a t e

Observed o r cu r ren t vacancy r a t e

Percent change i n r e n t

P r i ce o f r en ta l accornmodati on, r en t

Cor re l a t i o n c o e f f i c i e n t

C o e f f i c i e n t o f determi na t i on

Mean l e v e l o f ren ts

Nominal r e n t

Populat ion s i ze

Quanti t y o f r en ta l housi ng suppl i e d

S t a t i s t i CS Canada

Un i ted States o f America

Level o f vacancies (number o f vacant un i t s )

CHAPTER ONE

INTRODUCTION

I n l a r g e urban areas, a two t o t h r e e percent vacancy r a t e i n

t h e p r i v a t e r e n t a l apartment sec to r i s supposed t o i n d i c a t e a

balanced market t h a t "provides r e n t e r s . . . w i t h reasonable

choi ce. . . " [Canada Mortgage and Housi ng Corporat ion, 1996, p. i ] . The vacancy r a t e i s t h e percentage o f u n i t s a v a i l a b l e f o r

immedi ate occupat ion a t a speci f i c p o i n t i n t ime. The balanced

market vacancy r a t e (BMVR) i s used by t r a d i t i o n a l housing

ana lys ts i n comparing two o r more urban areas (Clayton Research,

1994). However, t h i s approach does n o t appear t o cons ider what

i mpact, i f any, v a r i ous soci O-economi c v a r i ab1 es coul d have on

t h e supply o f and demand f o r u n i t s i n t h e p r i v a t e r e n t a l

apartment s e c t o r . An a l t e r n a t i v e approach i s t o use t h e na tu ra l

vacancy r a t e (NVR).

Gabr ie l and N o t h a f t (1988, pp. 420-421 ) d e f i n e t h e n a t u r a l

vacancy r a t e "as t h a t [vacancy] r a t e a t which r e a l r e n t

i ncreases equal zero. " I n t h e i r mode1 , Rosen and Smith (1983,

p.784) assume t h a t d i f ferences between c i t i e s , i n such f a c t o r s as

government regu l a t i o n s , "have had s u f f i c i en t t ime t o have

a f f e c t e d t h e market t t . Th is suggests t h a t t he NVR i s p r e f e r a b l e t o

t h e balanced market vacancy r a t e as a market i n d i c a t o r because i t

consi ders v a r i ous soc i O-economi c and demographi c v a r i ab1 es.

S i nce t h e NVR takes i n t o cons ide ra t i on government

regu la t i ons , among o t h e r f ac to rs , i t may be use fu l i n eva luat ing,

modi f y i ng o r devel op i ng po l i cy. Therefore, t he NVR cou l d be used

i n con junc t ion w i t h t h e observed vacancy ra te , t o determine i f a

c e r t a i n po1 i c y o r group o f po1 i c i e s have s a t i s f i e d any goals o r

c r i t e r i a . I n terms o f urban p lanning, t h e NVR, when a p p l i e d t o

1

s p e c i f i c areas o f a mun i c i pa l i t y o r t o s p e c i f i c dwe l l ing types

could be use fu l i n encouraging and/or p r o t e c t i n g those

developments t h a t he lp t o balance t h e market. This i s impor tant

s i nce i t i s i 1 l e g a l i n Ontar io to recommend o r deny development

app l i ca t i ons on t he bas is o f tenure.

The i n t e n t o f t h i s research i s t o t e s t t he NVR as a market

i n d i c a t o r and t o evaluate t he determinants o f the NVR. The study

complements prev ious work on the NVR by Smith ( 1 9 7 4 ) , Rosen and

S m i t h (19831, Gabr ie l and Nothaf t (1988) and others, and r e l i e s

on t h e empi r i ca l framework l a i d ou t by these authors. Several

l i m i t a t i o n s o f t h e study and suggestions fo r f u t u re research w i l l

a l so be presented.

CHAPTER TM)

REVIEW OF THE LITERATURE

2 . 1 Overview

The focus o f t h i s rev iew o f t h e 1 i t e r a t u r e w i 11 be on t h e

r e l a t i o n s h i p between t h e pr ice-ad justment process and t h e NVU as

d iscussed i n t he i n t r o d u c t i o n . The l i t e r a t u r e review w i l l f o l l o w

t h e e v o l u t i o n o f research methodology as i t app l i es t o t h e above

r e l a t i o n s h i p . Beginning w i t h Smith (l974), t h e review w i 11 then

focus on t h e impor tant work by Rosen and Smith (1983) which forms

t h e b a s i s of t he works t o f o l l o w . Gabr ie l and Notha f t (1988) and

Reece (1988) attempt t o suppor t and extend t h e r e s u l t s o f Rosen

and Smith (1983 ) . An a l t e r n a t i v e use o f t h e NVR i s proposed by

Jud and Frew ( 1990 ) .

2.2 S tud ies and Results

Smith (1974) and Rosen and Smith (1983) bo th hypothesised

t h a t changes i n r e n t s were a f f e c t e d by vacancy ra tes . U t i l i z i n g

annual r e n t a l r e s i d e n t i a l da ta f o r f i v e Canadian c i t i e s f o r t h e

1961 t o 1971 per iod, Smi th ( 1 9 7 4 ) used a m u l t i p l e l i n e a r

regress ion t o test t h e above hypothesis. Rosen and Smith (1983)

used a pool ed c ross -sec t i on ti me-seri es anal y s i s f o r t h e years

1969 t o 1980 f o r 17 American c i t i e s . T h e i r regress ion equat ion i s

sirni l a r t o t h a t p u t f o rward by Smith ( 1 9 7 4 ) . The r e s u l t s o f bo th

s t u d i es i nd i cated t h a t vacanci es a re s i g n i f i can t i n exp l a i n i ng

percentage changes i n r e n t s a t t h e 95 percen t l e v e l (Smith, 1974,

p . 480; Rosen and Smith, 1983, p. 781 ) . Rosen and Smith a l s o

exami ned t h e NVR f o r t h e above 17 c i t i e s .

A NVR was c a l c u l a t e d f o r 14 o f t h e 17 c i t i e s - a reasonable

NVR cou ld n o t be c a l c u l a t e d f o r t h r e e o f t h e c i t i e s because

e i t h e r t h e mode1 d i d n o t h o l d f o r those c i t i e s o r t h e NVR seemed

3

"unreasonably h igh t t (p. 783). Rosen and Smith (1983) a l s o

hypothesised t h a t the NVR i s a f u n c t i o n o f c i t y s i r e , average

ren t , average annual change i n popu la t i on and t o t a l housing

stock, r e n t e r m o b i l i t y ( t he percent o f r e n t e r s moving i n a g i ven

year) , and t h e d i s p e r s i o n o f ren ts . M u l t i p l e l i n e a r regress ion

was used t o es t ima te t h e NVR. The r e s u l t s i n d i c a t e d t h a t t h e NVR

i s higher i n c i t i e s t h a t experience a h ighe r degree o f t u r n o v e r

( t he number o f u n i t s be ing vacated d u r i n g a s p e c i f i c t ime

per iod) . An ex tens ion o f Rosen and Smi th ' s work was c a r r i e d o u t

by Gabr ie l and N o t h a f t (1988).

Gabr ie l and Nothaf t (1988) used rne t ropo l i tan vacancy r a t e

data cornpiled by t he Bureau o f Census r a t h e r than us ing p r i v a t e

rea l es ta te data. Data was c o l l e c t e d f o r 16 U.S. m e t r o p o l i t a n

areas f o r t h e years 1981 t o 1985. Gabr ie l and Nothaf t (1988, p .

421 ) de f ined t h e NVR "as t h a t r a t e a t which r e a l r e n t increases

equal zero. ' ' It was hypothesized t h a t r e a l r e n t s would respond t o

excess supply o f o r demand f o r r e n t a l housing. NVRs were

e s t i mated by u s i ng a pooled c ross-sec t i on t i me-seri es anal y s i S .

Two types o f NVRs were ca lcu la ted : 1) exogenous, where t h e r a t e

i s in f luenced by f a c t o r s externa l t o t h e study area; and 2 )

endogenous, where t h e vacancy r a t e i s i n f l uenced by f a c t o r s

in te rna1 t o the area. The research f i n d i n g s concurred w i t h Smith

(1973) and Rosen and Smith ( l983) , i n t h a t changes i n r e a l r e n t s

were s e n s i t i v e and p o s i t i v e l y c o r r e l a t e d t o dev ia t i ons i n t h e

cur ren t vacancy r a t e from t h e NVR.

Reece (1988) s e t o u t t o expand upon t h e research done by

Rosen and Smith (1983). H i s a i m was t o p r o v i d e a d d i t i o n a l

evidence i n suppor t o f t h e pr ice-ad justment mechanism as p u t

forward by Rosen and Smith (1983, pp. 779-780). To t h i s end,

Reece u t i l i zed annual r e s i d e n t i a l da ta s e r i e s f o r seven U.S.

c i t i e s t h a t predated t h e t i m e p e r i o d used i n Rosen and Smith

(1983). A m u l t i p l e l i n e a r regress ion w a s used t o es t imate t h e

p r i c e s o f r e n t a l u n i t s . The r e s u l t s o f t h e regress ion c o n f i rmed

t h a t t h e c u r r e n t vacancy r a t e was a s i g n i f i c a n t v a r i a b l e i n

exp la in ing changes i n r e n t . (Reece 1988, pp. 412-415)

In a depar tu re from p rev ious research, Jud and Frew (1990)

focused on an a d d i t i o n a l v a r i a b l e . They hypothesised t h a t t h e

more a t y p i c a l ( d i f f e r e n t i n terms o f q u a l i t y and fea tu res ) an

apartment u n i t , t h e h igher t h e NVR f o r t h a t u n i t . Data w a s

c o l l e c t e d f rom two surveys o f apartment p r o j e c t s i n t h e

Greensboro Met ropo l i tan Area were conducted between 1988 and

1989. An annual mai l-survey asked, among o the r t h i n g s , t h e number

of apar tments a v a i l a b l e f o r r e n t and the q u a l i t y o f t h e

apartments (Jud and Puryear, 1989). A mu1 t i p l e 1 i near regress ion

w a s used t o est imate the NVR. The r e s u l t s showed t h a t t h e more

a t y p i c a l an apartment u n i t , t h e h igher t h e NVR and t h e h igher t h e

r e n t assoc ia ted w i t h t h a t u n i t . An examination o f t h e inferences

made by the var ious authors f o l l o w s .

2 .3 In fe rences and C r i t i q u e s

The main in fe rence made i s t h a t changes i n r e a l r e n t a re

p o s i t i v e l y c o r r e l a t e d t o t h e d i f f e r e n c e between t h e c u r r e n t

(observed) vacancy r a t e and t h e NVR (Smith, 1974; Rosen and

Smith, 1983; Gabr ie l and Notha f t , 1988; and Reece, 1988).

A d d i t i o n a l l y , i t i s a lso i n f e r r e d by these authors t h a t t he NVR

i s d i f f e r e n t f o r each m u n i c i p a l i t y . Rosen and Smith (1983, pp.

783-784) suggested t h a t t h i s i s p a r t l y due t o t h e t 'mob i l i t y o r

market t u rnove r o f tenants1' and t h a t d i f ferences between c i t i es,

such as government regu la t ions , "have had s u f f i c i e n t t i m e t o have

a f f e c t e d t h e market1'. However, despi t e concur r ing w i t h Rosen and

Smith (1983) and t h e i r pr ice-ad justment mechanism, Reece (1988)

pondered i f t h e r e was a need t o more p r e c i s e l y e x p l a i n t h e e f f e c t

o f changes i n r e n t on p r i c e expectat ions.

Beyond t h e cornmon theme o f a r e l a t i o n s h i p between r e n t a l

p r i ces , c u r r e n t vacancy r a t e s and t h e NVR, l i t t l e was o f f e r e d i n

terms o f p o s s i b l e exp lanat ions and fu tu re research d i r e c t i o n s .

Rosen and Smith (1983) b r i e f l y mentioned i n a f o o t n o t e t h a t t h e

NVR model d i d no t ho ld f o r two o f t h e c i t i e s and t h a t t h e NVR was

t oo h igh f o r another. There was no attempt t o e x p l a i n these

f a i l u r e s o f t h e model. Th i s leaves t h e model open t o c r i t i c i s m .

Gabr ie l and Nothaft (1988) o n l y went as f a r as suppor t ing

t h e above r e l a t i o n s h i p as proposed by Rosen and Smith (1983).

Reece (1988, pp. 416-417) d i d suggest t h a t p r i c e expectat ions may

p l a y a r o l e i n t h e pr ice-adjustment mechani sm, bu t , t h a t ' 'the

task o f mode l l ing p r i c e expec ta t ions" would be a d i f f i c u l t

exerc i se due t o t h e " l a rge number o f p a r t i c i p a n t s i n t h e housi ng

market. " 3ud and Frew (1990) went beyond t h e p r i c e mechani sm-

vacancy r a t e hypothesi s by exami n i ng t he r e l a t i onshi p between t h e

a t y p i c a l i t y o f r e n t a l u n i t s and t h e l e v e l o f t h e NVU.

Jud and Frew (1990, pp. 300-301) i n f e r r e d t h a t changes i n

r e n t were i n v e r s e l y r e l a t e d t o t h e r a t e o f vacancy i n t h e

previous pe r i od . They also s t a t e d t h a t " the more t y p i c a l an

apartment u n i t , t h e lower t h e n a t u r a l r a t e o f vacancy." However,

there w a s no attempt t o e x p l a i n these r e l a t i o n s h i p s . Despi te

t h i s problem, Jud and F r e w (1990) e x h i b i t e d how t h e NVR may be

used f o r speci f i c market segments and speci f i c dwel 1 i ng types.

2 . 4 Summary

The a p p l i c a t i o n o f NVRs t o t he p r i v a t e r e n t a l apartment

market has several strengths, inc lud ing , the p o s s i b i l i t y t o

est imate speci f i c NVRs f o r s p e c i f i c urban areas, and s p e c i f i c

market segments such as townhouse apartments. Among t he

weaknesses, t h e i mpact o f government regul a t i ons on ren ts i s not

c l ea r i n the 1 i te ra tu re , and t h e lack of representa t ive data f o r

a study area cou ld understate o r overstate the NVR leading t o

f a l s e inferences and/or statements.

Despite these weaknesses, which t h i s paper w i l l not attempt

t o c o r r e c t , t he NVR model, as described by Rosen and Smith

(1983) and Gabr ie l and Nothaf t (1988), w i l l form the

methodological approach t o be used i n the thes i S . Un1 i ke the

ma jo r i t y o f prev ious work, t h e exception being Smith (1974) , t h i s

study wi11 use Canadian data t o t e s t these models.

CHAPf ER THREE

A PRIORI MODEL

3.1 P r i ce-Ad justment Mechani s m

The a p r i o r i model (F igu re 1 ) t o be used i n t h i s t h e s i s i s

based on t h e t h e o r e t i c a l and emp i r i ca l work done by Rosen and

Smith (1983). The work o f o t h e r researchers (Hendershott and

Haurin, 1988; Gabr ie l and No tha f t , 1988; Jud and Frew, 1990) i s

al so i ncorporated i n t o t h i s model where noted. The model used by

Rosen and Smith (1983) i s an example o f a pr ice-adjustment

mechanism. Th i s mechanism a t tempts t o show how a p r i c e of a good

o r se rv i ce i s changed i n response t o changes i n sorne predef ined

s e t o f va r i ab les . Rosen and Smith (1983, p. 779) i d e n t i f i e d t h e i r

mode1 as the " r e n t a l pr ice-adjustment mechani sm. "

The p r i ce-adjustment mechani sm and t h e r e n t a l housi ng market

operate i n a s tock- f tow manner. A t any one t ime t h e r e i s a

q u a n t i t y of r e n t a l housing u n i t s supp l ied and demanded. Rosen and

Smith (1983) suggested t h a t demand, O , i s a f u n c t i o n o f t h e

p r i c e o f r e n t a l accommodation ( r e n t ) , RNT, and o t h e r f a c t o r s , F,

(such as t h e c o s t o f homeownership, r e a l income per household,

and demographic v a r i a b l e s ) , as s e t out i n :

(1 ) D = d(RNT,F) .

The q u a n t i t y o f r e n t a l housing suppl ied, S, i s dependent,

among o ther f a c t o r s , on t h e l e v e l o f r e n t . Ho ld ing these o ther

f a c t o r s constant , t h e h ighe r r e n t , t h e g rea te r t h e i n c e n t i v e t o

i n t roduce new u n i t s t o t h e market. However, i n t h e s h o r t term t h e

q u a n t i t y o f u n i t s supp l ied i s assumed t o be f i x e d . The l e v e l of

vacanci es, VL, i s t h e d i f ference between t h e quant i t y demanded

and suppl i ed :

( 2 ) VL=S-O.

FIGURE 1 RENTAL PRICE-ADJUSTMENT MECHANISM

Units Vacant

471 Tl Real Incorne - 7 ' Demographic

Observed Vacancy Rate

(OVR) V

Owning

Units Demanded

Natural Vacancy Rate

(NVR) Vn

Per Household

Rental Price Adjustment Mechanism

OVR < NVR (; ~ o v R > f U v R

Variables

I I 1 Source: Author. 1998.

9

Rent Conf rot

No Change 1

+ lncrease OVR = NVR Decrease Rent Rent

The observed o r cu r ren t vacancy r a t e (OVR), V, i s t h e number o f

vacant u n i ts , VL, d i v i ded by t h e q u a n t i t y of r e n t a l u n i t s

suppl ied, S:

( 3 ) V = VL/S = 1-(1/S) * d(RNTjF)

The r e n t a l p r i c e adjustment mechanism i s o u t l i n e d i n

equat ion 4 and i s based on Gabr ie l and N o t h a f t ' s (1988, p. 421)

modi f i c a t i on o f Rosen and Smith ' s (1 983) research. Devi a t i ons i n

the OVR f rom t h e NVRj Vn , determines changes i n t h e r e a l r e n t o f

rental u n i t s . The r a t e o f change, g, i n nomi na1 ren ts , R n , i s a

f u n c t i o n o f t h e d i f f e rence between the NVR and t h e OVR:

( 4 ) Rn = g(Vn-V).

It i s assumed t h a t over t h e es t ima t i on p e r i o d t h e NVR i s

constant b u t v a r i e s according t o market c o n d i t i o n s and t h a t Vn

may be i ncorporated i n t o t h e i n t e r c e p t . T h e e s t i m a t i n g model i s

w r i t t e n as:

( 5 ) PCR = (be ta X ) + b iV

where PCR i s t h e percent change i n ren t , b e t a X i s t h e i n t e r c e p t

and b i i s t h e s lope. I n a d d i t i o n t o t h e above s p e c i f i c a t i o n ,

Rosen and Smith (1983) among others , pooled da ta cross-sect ion

t i m e - s e r i es regress ion were est imated w i t h c i t y dummy v a r i ables.

This poo led da ta model i s w r i t t e n as:

S - l

(6) PCR = (be ta X ) + C b j c j + b i V j = I

where N i s t h e number o f c i t i e s pooled i n t h e ana l ys i s , bj a r e

regress ion c o e f f i c i e n t s and c j are t h e area dummy va r i ab les . NVR

i s t h e r a t e a t which changes i n real r e n t s a r e equal t o zero.

From equat ion 6 t h e NVR can be i n t e r p r e t e d as f o l l o w s :

( 7 ) V n i = (be ta X + b i ) / b i .

I n t h e s h o r t r u n i t i s assumed t h a t t h e NVR i s cons tan t .

Di f ferences between t h e OVR and t h e NVR r e f l e c t e i t h e r an excess

supply o f r e n t a l housi ng (NVR i s l e s s than OVR) o r an excess

demand f o r r e n t a l housing (NVR i s g rea te r than OVR). I n t h e

former case, r e n t s should inctease, whereas i n t h e l a t t e r case,

r e n t s should decrease. I f the NVR equals t h e OVR, r e n t s should

no t change. A f o u r t h op t i on i s found i n t h e form o f r e n t c o n t r o l .

R e n t c o n t r o l breaks t h e 1 i nkages i n t h e pr ice-adjustment

mechani sm. Typi c a l r e n t c o n t r o l l e g i s l a t i o n 1 i m i t s t h e number o f

t imes r e n t can be increased i n a g iven p e r i o d and/or t h e amount

o f t h a t increase (Smith and Tomlison, 1981, pp. 94-97). Thus, i t

i s no t always p o s s i b l e t o increase r e n t t o the l e v e l suggested by

t h e pr ice-adjustment mechanism. These changes, i f any, i n ren ts ,

loop back t o t h e s t a r t o f t he mechanism and a f f e c t t h e q u a n t i t y

of u n i t s supp l i ed and demanded.

3 .2 Rat iona le

The r a t i o n a l e f o r us i ng t h e proposed model i n F i g u r e 1 and

t h e accompanying equations i s based l a r g e l y on t h e acceptance of

the Rosen and Smith (1983) model i n t h e 1 i t e r a t u r e . L i t e r a l 1y

every author i n t h i s f i e l d has used t h e Rosen and Smith model as

t h e bas is o f t h e i r research (Gabr ie l and Nothaf t , 1988;

Hendershott and Haur in, 1988; Read, 1988; Reece, 1988; V o i t h and

Crone, 1988; Wheaton and Torto, 1988; 3ud and Frew, 1990). These

authors d i d no t employ the model exp l i c i t l y - changes were made

t o r e f l e c t t h e na tu re o f t h e i r s p e c i f i c research o b j e c t i v e s . Th is

demonstrates t h e v e r s a t i l i t y o f t h e model f o r o the r research

purposes. For example, Vo i th and Crone (1988), Wheaton and Tor to

(1988) and Benjamin e t a l (1997) used t h e Rosen and Smith model

t o est imate NVRs f o r t h e commercial o f f i c e sec to r . I n a d d i t i o n ,

no l i t e r a t u r e has been found t h a t r e f u t e s o r chal lenges t h e work

performed by Rosen and Smith. The l a c k o f any chal lenge t o t h i s

model i s a s t r o n g i n d i c a t o r t h a t t h e mode1 i s a sound one. That

sa id , t he re i s a need t o t e s t t he model us ing cu r ren t da ta f o r

Canadian urban areas.

3.3 L i m i t a t i o n s o f the model

Despi t e t h e smooth fl ow o f t he model dep ic ted i n F igu re 1,

t h e r e n t a l housing market i s sub ject t o t i m e lags and government

regu la t i on . Tenants t y p i c a l l y s ign leases o f 12 months. I n t h e

Province o f Ontar io , p r i o r to June 1998, l e g i s l a t i o n requ i red

t h a t a tenant p r o v i d e two months n o t i c e p r i o r t o vaca t ing t h e

u n i t , pe rm i t t ed one increase i n r e n t p a i d per 12 month per iod ,

and l i m i t e d t h e amount o f t h a t increase. A s of June 1998, t h e

Province of On ta r i o brought i n a systern o f vacancy decont ro l .

Under t h i s system, when a u n i t becomes vacant, t he re i s no cap on

t h e rent t h a t may be charged. Once t h e u n i t i s occupied r e n t

cont r o l appl i es and r e n t i ncreases a r e regu l ated. The Prov i nce

expects t h a t t h i s new system o f r e n t c o n t r o l w i l l encourage t h e

cons t ruc t i on o f r e n t a l u n i t s i n Ontar io . Th i s may reduce t h e tirne

l ags and t h e degree o f government i n t e r v e n t i o n i n t h e r e n t a l

housi ng market.

3.4 Hypotheses

Based on t h e o b j e c t i v e s o f t h i s s tudy, t h e review o f t h e

l i t e r a t u r e and t he a p r i o r i model, t h e f o l l o w i n g hypotheses w i l l

be eval uated :

1. A f u n c t i o n a l r e l a t i o n s h i p e x i s t s between the percent change i n r e n t and t h e observed vacancy r a t e .

2 . The n a t u r a l vacancy r a t e i s a f u n c t i o n o f : i ) t h e mean l e v e l of ren ts ; i i ) popu la t i on size; i i i) r e n t e r mobi 1 i t y ra te ; i v ) t h e average annual change i n t o t a l housing stock; and v ) the average annual growth i n popu la t i on .

The f i r s t hypothesi s i s based on the p r i ce-adj ustment mechani s m

mode1 forwarded by Rosen and Smith (1983) . The second hypothesis

i s based on Rosen and Smith (1983) and Gabriel and Nothaft (1988)

who in fe r red that the population o f a c i t y and the m o b i l i t y of

t h a t population have an impact on the l e v e l o f the NVR.

CHAPTER FOUR

METHODOLOGY

4 . 1 Areas o f study

The areas o f s tudy i n F igure 2 cons i s t o f s i x ce nsus

m e t ropol i tan areas (CMA) : Hami 1 ton, K i tchener, London, Sudbury,

S t . Catharines-Niagara and Windsor, and four census

aggl omerati ons (CA) : B a r r i e, Guelph, K i ngston and Peterborough,

a l 1 i n t he Province of Ontar io. The s i t e s a re in f luenced by

surroundi ng areas i n two ways: 1 ) employrnent opportuni t i e s ; and

2) housing cos ts . The in f luence o f surrounding areas i s m i n imized

by using t he CMA as t h e bas is f o r d e f i n i n g a study area.

The use o f t h e CMA/CA as a means o f d e f i n i n g t h e study area

i s j u s t i f i e d as f o l lows. The S t a t i s t i c s Canada (StatCan)

d e f i n i t i o n o f a CMA/CA i s based on place-of-work data. Data i s

r e a d i l y a v a i l a b l e a t t h e CMA/CA l e v e l . CMHC, StatCan and var ious

housi ng anal ysts ( C l ayton, 1994) u t i 1 i ze t h e CMA/CA when

comparing housing market i nd i ca to r s between urban areas. The

var ious works discussed i n Chapter Two used the CMA/CA, o r

equi valent, i n t h e i r ana lys i s o f the NVR (Smith, 1974; Rosen and

Smith, 1983; Gabr ie l and Nothaf t , 1988; and Reece, 1988).

4 . 2 Sampling frame

The sampling frame f o r t h i s mode1 i s based on t h e da ta

gathered by t he CMHC and StatCan, and mod i f i ed as requ i red . The

CMHC c o l l e c t s and disseminates r e n t a l market data f o r every

CMA/CA i n Canada. Th is i s not a complete populat ion. The survey

on l y i n c l udes those r e n t a l u n i t s i n b u i l d i n g s w i t h s i x o r more

u n i t s , as de f ined by CMHC, and was, u n t i l recent ly , c o l i e c t e d

semi-annually. The s tudy pe r iod i s f rom 1988 t o 1996.

Windsor CMA

LEGEND

Study Areo - CMNCA As defined by Statistics Canada

Source: Statistics Canada. 1 992. O 0 O 120 *M.

O 4 O 80 MI.

Cur ren t l y , data i s c o l l e c t e d d u r i n g t h e month o f October each

year and t h e survey now inc ludes r e n t a l u n i t s i n b u i l d i n g s w i t h

t h r e e o r more u n i t s .

A d d i t i o n a l l y , CMA/CA boundaries change over t ime, there fo re ,

i t i s necessary t o know when boundary changes occurred, what

e f f e c t t h i s had on t h e sample s i r e , and what adjustments, i f any,

t o p rev ious data had been c a r r i e d out . StatCan da ta i s a lso

sub jec t t o s imi l a r problems i n terms o f changes i n CMA/CA

boundaries. The r a t i o n a l e f o r u t i 1 i z i n g t h i s sampl i n g frarne i s

based on the fac t t h a t t h e above agencies have i n p lace a system

o f sampling procedures and des ign t h a t i s c o n s t a n t l y be ing

moni tored f o r e r ro rs , changes and improvements.

4.3 Data collection

The fi r s t hypothesi s, t h a t t h e percent change i n r e n t i s a

f unc t i on o f t he d i f f e r e n c e between the NVR and OVR, was

eval uated by us i ng c l ass i c a l regress ion anal ys i s on i nd i v i dual

areas and a m u l t i p l e regress ion ana l ys i s on t h e pooled da ta .

Four assumpti ons associ a t e d w i t h c l assi c a l r eg ress i on anal y s i s

a re as f o l l o w s : 1) t h e reg ress ion ana lys is f i t s a s t r a i g h t l i n e

through t h e s c a t t e r p l o t o f da ta po in ts ; 2 ) f o r every va lue o f t h e

i ndependent va r i ab le ( x ) , t h e d i s t r i b u t i o n o f r e s i d u a l values (Y-

Y i ) should be normal l y d i s t r i b u t e d w i t h zero means; 3 ) t ha t no

a u t o c o r r e l a t i o n ex i s ts ; and 4 ) homoscedastici t y i s present .

The vacancy r a t e and r e n t da ta was obta ined from CMHC

p u b l i c a t i o n s . The percent change i n r e n t was based on an average

o f t h e mean ren ts p a i d f o r a one-bedroom and two-bedroom p r i v a t e

r e n t a l apartment u n i t i n b u i l d i n g s w i t h s i x o r more u n i t s . 00th

v a r i a b l e s a re f o r t h e month o f October.

I n a d d i t i o n t o t h e above data, t h e pooled da ta ana lys is used

ni ne dummy v a r i ab1 es. Each dummy v a r i ab1 e represented a speci f i c

area of study. The t e n t h area, Windsor, was i n d i c a t e d by a l 1 n ine

dummy v a r i ab1 es hav i ng a v a l ue o f zero.

The second hypothes is , t h a t t h e NVR i s a f u n c t i o n o f var ious

v a r i ables, u t i 1 i zed a m u l t i p l e regress ion a n a l y s i S . A t - t e s t was

used t o t e s t v a r i a b l e s f o r s ign i f i cance (Rosen and Smith, 1983;

Hendershott and Haur in, 1988, p . 346; Gabr ie l and Nothaf t , 1988).

Based on t h e work by Rosen and Smith (1983), t h e ad justed mode1

t o est imate t h e determinants o f t h e NVR i s :

( 8 ) Vn = ~ (Rrn j PS, MOB, cSH, cPOP)

where Rm i s t h e mean l e v e l of ren ts , PS i s t h e popu la t ion s ize ,

MO6 i s t he r e n t e r m o b i l i t y r a t e , cSH i s t h e average annual

change i n t o t a l housing stock, and cPOP i s t h e average annual

growth i n popu la t ion . Given a confidence l e v e l o f 95 percent and

degrees o f freedorn equal t o n-2 where n i s t h e sample s ize, i f t

observed exceeds t - c r i t, w e r e j e c t t h e nu l 1 hypothesi s and i nfer

t h a t t h e i ndependent v a r i a b l e i s s i g n i f i c a n t .

The NVR was c a l c u l a t e d us ing equat ion ( 7 ) and data from t h e

fi r s t hypothesis. The mean l e v e l of r e n t s was t h e average r e n t

over t h e study p e r i o d . Populat ion s i z e and average annual growth

i n popu la t ion data were obta ined from t h e Census o f Canada. The

r e n t e r m o b i l i t y r a t e was based on rnover data. T o t a l occupied

household data was used as a proxy f o r t o t a l housing stock. I n

t h e Census, one household equals one occupied dwe l l i ng . Th is

method w i l l underest imate t h e t o t a l housing s tock, however, i n

t h e 1991 Census, p r i va te unoccupi ed dwel 1 i ngs accounted f o r no

more than 6.4 percent o f t o t a l p r i v a t e d w e l l i n g s o f t he s i x CMAs

i n t h i s study ( S t a t i s t i c s Canada, 1992).

CHAPTER F I V E

RESULTS AND DISCUSSION

5.1 Overview

The chapte r w i 11 f i r s t p resen t t h e r e s u l t s o f t h e f i r s t

hypothesi s i n regards t o t h e r e n t a l pr ice-adjustment mechani sm

i n c l udinç i n d i v i d u a l regress ions f o r each study area and t h e

pooled data reg ress ion . Th is i s f o l lowed by t h e c a l c u l a t i o n o f

t h e NVR f o r each area o f s tudy. The t h i r d sec t i on w i l l present

t h e r e s u l t s o f t h e second hypothes is i n regards t o t h e

determinants o f t he NVR. Concluding thoughts about t h e r e s u l t s

a r e o f f e r e d i n t h e f i n a l s e c t i o n .

5 .2 Hypothesi s One - Rental P r i ce-Adjustment Mechani sm

A summary i s prov ided i n Tables 1 and 2 on t h e f o l lowing

page f o r t h e i n d i v i d u a l study area regress ions and t h e pooled

data regress ion, r e s p e c t i v e l y . Deta i l e d s t a t i s t i c a l r e p o r t s a re

prov ided i n Appendices A and B.

5 .2 .1 I n d i v i d u a l Regressions

The t e s t assumptions o f t h e regress ion analyses were

s a t i s f i ed. However, i n t he case o f t h e i nd iv idua l regressions,

t h e Durbi n-Watson s t a t i s t i c i nd ica tes t h a t some p o s i t i v e

a u t o c o r r e l a t i on does ex i s t f o r B a r r i e , Hami 1 ton, K i tchener and

Sudbury. There i s a poss ib i 1 i t y o f temporal c o r r e l a t i o n , s ince a

r e n t a l u n i t may be vacated and leased several t imes d u r i ng the

study pe r i od . S ince the sample s i z e i s small i n the i n d i v i d u a l

regress ions - o n l y e i g h t observa t ions - i t i s d i f f i c u l t t o i n f e r

t o what degree a u t o c o r r e l a t i o n e x i s t s , i f a t a l l . Due t o t ime

cons t ra i n t s , no c o r r e c t i o n f o r a u t o c o r r e l a t i o n was made i n t h i s

study. i t should be noted t h a t p r e c i s i o n o f t h e r e s u l t s m a y be

reduced.

18

TABLE 1 INDIVIDUAL REGRESSIONS SUMMARY

HYPOTHESIS ONE

Barrie CA .- - - -

Guelph CA

Hamilton CMA - - -

Kingston CA

Kitchener CMA -

London CMA

Peterborough CA

St-Catharines-Niagara CMA - " -

Sudbury CMA

Windsor CMA

Dependent Variable: lndependent Variable: Source: Author, 1998.

Percent Change in Rent Vacancy Rate

TABLE 2 POOLED DATA REGRESSION SUMMARY

HYPOTHESIS ONE

I F ( ~ O. 69) = 3.643 p < 0.001; Durbin-Watson = 1.71 3

Dependent Variable: Percent Change in Rent N=80 Independent variables: 10; Vacancy Rate plus nine Dummy Variables Source: Author, 1998.

NVR

- -

4.14

4.92

4.75

4.97

5.97

6.43

6.22

6.81

6.28

5.30

Variable

Constant

Vacancy Rate - .-

Barrie CA

Guelph CA

Hamilton CMA - - .

Kingston CA

Kitchener CMA . .

London CMA -

Peterborough CA

St-Catharines-Niagara CMA

Sudbury CMA

Windsor CMA

R = 0.588; R' = 0.346; Adjusted - R'= - - 0.251 - - .

b t (69) Sig.

0.0654 6.966 100.0% - -

-0.01 23 -5.895 100.0%

-0.0143 -1 -220 77.3% - -

-0.0047 -0.399 30.9% - -

-0.0068 -0.582 43.8%

-0.0004 -0.035 2.8%

0.0083 0.707 51.8%

- 0.01 39 1.148 74.5%

0.01 14 0.953 65.6% - --

0.01 85 1.533 87.0%

0.01 21 1 .O36 69.6%

- - -

The r e s u l t s o f our est imat ion i n d i c a t e t h a t the vacancy r a t e

was s i gni f i c a n t i n exp la i n i ng the percentage change i n r en t s a t

the 90 percent l e v e l i n s i x o f t h e t en areas: iiami l t o n , Kingston,

London, Peterborough, S t . Cathari nes and Sudbury. The resu l t s f o r

Guelph and Windsor were s i gni f i can t a t t he 75 percent 1 evel ,

based on seven degrees o f freedom and a t - c r i t i c a l value o f

0 . 7 1 1 . Therefore, a t t he 75 percent l e v e l e i ght out o f t e n areas

had s i g n i f i c a n t resul t s . The r e s u l t s fo r Ba r r i e and Ki tchener

were i n s i gni f i cant . The regress i on c o e f f i c i e n t s f o r a l 1 ten areas had negat i ve

s igns. T h i s i nd ica tes t h a t an increase i n t he current vacancy

r a t e above the na tu ra l vacancy r a t e should r e s u l t i n a srnaller o r

negative percent change i n ren t . This i s consis tent w i t h supply

and demand theory, i n general, and w i t h Rosen and Smith (1983)

and Gabriel and Nothaf t (1988). I n Hamilton, London, S t .

Cathari nes and W i ndsor the regressi on coef f i c i ents i ndi ca te t h a t

vacancies are more sens i t i ve t o changes i n ren ts than t h e

remai n i ng areas. A sens i t i ve r e l a t i onshi p suggests t h a t

landlords are more responsive t o the vacancy ra te . For example,

if the vacancy r a t e increases, land lords i n these areas are more

1 i kel y n o t t o i ncrease the ren t . The es t imat ion produced the best r e s u l t s fo r S t . Catharines

w i t h a c o r r e l a t i o n c o e f f i c i e n t , R , of 0.957, i n d i c a t i n g a s t rong

and d i r ec t r e l a t i onshi p between the i ndependent and dependent

var iab les, and a c o e f f i c i e n t o f determinat ion, R 2 , o f 0.916. The

independent var iab le , vacancy ra te , exp la ins almost 92 percent of

the t o t a l v a r i a t i o n i n the dependent v a r i able, percent change i n

r e n t . The R and R2 values should be t r ea ted w i t h caut ion. A h igh

R* va l ue may i ndi ca te co l 1 i near i t y between the i ndependent and

dependent v a r i ab1 es. Other areas w i t h s t r o n g r e s u l t s i n c l ude

K i ngston, London and Sudbury. Hami 1 t o n and Peterborough had

moderate c o r r e l a t i o n s c o e f f i c i e n t s , whi l e B a r r i e , Guelph,

K i tchener and Windsor had weak values.

5.2.2 Pooled Data Regression

Table 2 r e p o r t s t h e regress ion r e s u l t s f o r equation ( 6 ) . The

mode1 exp la ins approx imate ly 35 percent o f t h e v a r i a t i o n i n t h e

percent change i n r e n t s . The c o r r e l a t i on c o e f f i c i ent, R,

i nd i cates a moderate d i r e c t r e l a t i onshi p between the vacancy r a t e

and percent change i n r e n t . The F-value o f 3 .64 i s s i g n i f i c a n t a t

t h e 0.01 l e v e l . A u t o c o r r e l a t i o n i s ve ry weak as i nd i ca ted by a

Durbin-Watson va lue o f 1.713. The c o r r e l a t i o n ma t r i x i n Appendix

8 shows very l i t t l e c o r r e l a t i o n between t h e observed vacancy r a t e

and t h e dummy v a r i a b l e s and between t h e percent change i n r e n t

and t h e dummy v a r i a b l e s .

Resul t s i n Tab le 2 i nd ica te t h a t t h e VR c o e f f i c i e n t has a

negat i ve s ign . That i s , a decrease i n t h e vacancy r a t e i s

associated w i t h an increase i n t h e pe rcen t change i n r e n t .

T h i s i s cons i s ten t w i t h t h e f i n d i n g s f rom t h e i n d i v i d u a l

regress ions above and w i t h Rosen and Smith (1983) Gabr ie l and

Nothaf t (1988) and Benjamin e t a l (1997).

5 .3 The Natura l Vacancy R a t e

The NVR was c a l c u l a t e d us ing equat ion ( 7 ) and regress ion

c o e f f i c i e n t s from t h e pooled data reg ress ion . The r e s u l t s a re

presented i n Table 2. The mean n a t u r a l vacancy r a t e i s 5.58

percent . There i s 1 i t t l e v a r i a t i o n i n t h e study area NVRs. Rates

range from a low o f 4.14 percent i n B a r r i e t o a h igh of 6.81 i n

St .Cathar ines, a d i f f e r e n c e o f 2 .67 percentage po in t s . T h i s i s

i n c o n t r a s t t o Rosen and Smith (1983, p. 783), Gabr ie l and

Nothaft (1988, p.425) and Benjamin e t a l (1997, p . Q ) , who found

considerable v a r i a t i o n among met ropo l i tan na tu ra l vacancy rates.

These values are higher than t he two t o t h ree percent

balanced market vacancy r a t e used by CMHC (1996, p . i ) , because i t

i s argued by Rosen and Smith (1983, p.784) t h a t d i f fe rences

between c i t i e s , such as munic ipal government regu la t ions ,

employment opportuni t i es, and t he devel opment envi ronment, have

had ample t ime t o a f f e c t the market. It should be noted t h a t t he

mean na tu ra l vacancy r a t e i s o n l y 2.5 percentage p o i n t s higher

than the balanced market vacancy r a t e used by CMHC and housing

analysts. Th is seems t o suggest t h a t t he BMVR cou ld be increased

t o between f i v e o r s i x percent f o r simple compari son purposes.

Before such a change i s made o r suggested, i t would be wise t o

evaluate t he est imat ing model i n equations (5 ) and (6 ) on

addi t i onal CMA/CAs throughout Canada.

5 .4 Hypothesis Two - Oeterminants o f t he Natural Vacancy Rate

The second hypothesis s t a ted t h a t t he NVR i s a funct ion o f :

i ) the mean l e v e l of rents; i i ) populat ion s i ze; i i i ) ren te r

mob i l i t y ra te ; i v ) the average annual change i n t o t a l housing

stock; and v ) t h e average annual growth i n populat ion. The

est imat ing model i s set out i n equation ( 8 ) . Resul ts o f the

analysis are summarized i n Table 3. A de ta i l e d s t a t i s t i c a l repor t

w i t h addi t i o n a l regression resu l t s and desc r i p t i ve s t a t i s t i c s i s

provided i n Appendix C. Caution should be used i n i n t e r p r e t i n g

these r e s u l t s . The regression ana lys is i s weak due t o a small

sample s i t e - ten observations f o r each o f t he f i v e regressors.

The regress i on has an R o f 0.81, i n d i c a t i ng a s t rong and

d i r e c t r e l a t i onshi p between the na tu ra l vacancy r a t e and t h e

independent var iab les . Almost 66 percent of t he v a r i a t i o n i n t h e

na tura l vacancy r a t e can be explained by t he independent

va r iab les . The Durbin-Watson value i s low a t 1.04, i n d i c a t i n g

there i s some p o s i t i v e au toco r re la t i on . Addi t i o n a l ly, t h e

c o r r e l a t i on ma t r i x i n Appendix C, revea l s some c o r r e l a t i o n

between several independent var iab les . The reader should be aware

t h a t t h i s may a f f e c t t he p rec i s ion o f t h e r e s u l t s . Due t o t ime

cons t ra in t s no co r rec t i on f o r au toco r re la t i on was perfotmed.

The s igns on mean rents , Rm, popu la t ion s i r e , PS, average

annual growth i n populat ion, cPOP, and t he m o b i l i t y r a t e , MOB,

are negative, suggesting t h a t h igher ren ts , l a rge r populat ions,

h igher popu la t ion growth and higher m o b i l i t y ra tes are assoc ia ted

w i t h lower NVRs. Average annual change i n housing stock has a

p o s i t i v e s i gn i n d i c a t i ng t h a t smal l e r changes i n housi ng s tock

are r e l a t e d w i t h lower NVRs. However, none o f t he va r i ab l es a r e

s i gn i f i c a n t a t the 95 percent l e v e l o r h igher .

TABLE 3 HYPOTHESIS TWO REGRESSION SUMMARY

R = 0.809: R'= 0.655; Adjusted R' = 0.225 - - - - - . - - - - - - - - -

F(5,4) = 1.522 p < 0.353; Durbin-Watson = 1 .O40

Dependent Variable: Natural Vacancy Rate Independent Variables: 5 - see above Source: Author. 1998.

5.5 D i scussi on

There seems t o be a func t iona l r e l a t i o n s h i p between t h e

percent change i n r e n t and the observed vacancy ra te . The pooled

data regression expla ined 35 percent o f t h e v a r i a t i o n i n t h e

percent change o f r e n t . The vacancy r a t e was found t o be

s i gni f i can t a t a p - leve l o f 0.05. However, none o f the dummy

v a r i ab1 e regress i on coef f i c i ents were s i gn i f i cant a t t he 95

percent 1 evel . The funct ion between the components ( o r determinants) of the

na tu ra l vacancy r a t e and t he l e v e l o f the na tu ra l vacancy r a t e i s

uncer ta in . Though t h e R value ind ica ted a s t rong and d i r e c t

r e l a t i onsh ip , t he re w a s a vast d i f f e r e n c e between the values of

R2 and the adjusted R * . Add i t i ona l l y , none o f the var iab les were

s i g n i f i c a n t a t t h e 95 percent l e v e l and t he re appeared t o be some

posi t i ve au toco r re l a t i on. Caution should be used i n i n t e r p r e t i n g

these values s ince t h e sample s i ze (N=10) was smal l .

A t f i r s t glance, i t appears t h a t t h e l a r g e r the popu la t ion ,

t h e stronger and more sensi t i ve t he r e l a t i onshi p between percent

change i n r en t and t h e vacancy r a t e i s . Th is holds t r u e fo r four

o f t he f i v e l a r g e s t areas i n the sample. However, there i s a weak

and i ns ign i f i c a n t r e l a t i onshi p f o r Ki tchener, t he t h i r d l a r g e s t

area i n terms o f popu la t ion i n the study.

A p l aus i b l e exp lanat ion may be the extens ive CO-operat ive

(CO-op) education programs o f fe red by t he Un i ve r s i t y o f Waterloo

( U W ) . O f the almost 24,000 students enro led a t U W , about 9,000 o r

38 percent are CO-op students (Un i ve r s i t y o f Waterloo, 1998). It

i s t y p i c a l f o r a CO-op student t o a l t e r n a t e between a term of

school and a term o f work, usual ly f o r f i v e years. S i nce i t i s

cornmon f o r the work term t o be done ou t s i de t h e Kitchener CMA,

some s tudents w i l l seek a four month lease i n s t e a d o f t he common

12-month lease.

To t h e l and lo rd , t h e i m p l i c a t i o n s o f CO-operat ive education

a r e a d d i t i o n a l costs i n regards t o a d v e r t i s i n g t h e u n i t , c r e d i t

and background checks, and r e p a i r i ng/c l eani ng t h e un i t every f o u r

months. To t h a t end, t h e l a n d l o r d may charge a lower r e n t

( e i t h e r a reduc t i on i n t h e a c t u a l r e n t p a i d o r a one-time rebate)

f o r longer- term leases i n o r d e r t o reduce t h e c o s t s mentioned

above, even if t h e pr ice-ad justment mechanism i n equations (6)

and ( 7 ) suggests a r e n t inc rease . That i s , t h e l and lo rd , i n

s e t t i ng t h e r e n t , i s more s e n s i t i v e t o reduc i ng costs than t o t h e

vacancy r a t e .

The poor r e s u l t s o f t h e i n d i v i d u a l and pooled data fo r

several o f t h e study areas may be due t o va r i ous fac to rs .

B e s i des t h e exp l anat ion d i scussed above f o r t h e K i tchener CMA,

another p o s s i b i 1 i t y i s t h e s i z e o f t h e p r i v a t e r e n t a l apartment

market. The d i v e r s i t y and qua1 i t y o f r e n t a l uni t s may be l i m i t e d

i n areas w i t h smal ler popu la t i ons . It i s p o s s i b l e t h a t a tenant

m a y f i nd a u n i t t h a t s u i t s t h e i r needs (number o f rooms,

l o c a t i o n , s i z e , and so on) . Since the market i s n o t as d iverse,

t he tenant m a y have t o pay a premi um f o r t h a t u n i t . Landlords,

b e i ng aware t h a t choice i s 1 i m i ted, are n o t necessar i l y

responsive t o changes i n t h e vacancy r a t e . T h i s p a r t l y exp la ins

t h e low regress ion c o e f f i c i e n t values f o r t h e areas w i t h t h e

smal les t popu la t ion .

CHAPTER S I X

CONCLUSION

obvious weaknesses w i t h t h i s r

6.1 L i m i t a t i o n s

One o f t h e mo esearch was

i t s r e l i a n c e on a very small sample s i r e due t o t ime, budget and

external cons t ra in ts . CMHC on l y began prov id ing ren ta l apartment

market data i n 1988. I n i t i a l l y , data was co l l ec ted

semi-annual l y each year f o r u n i t s i n bu i l d ings w i t h s i x o r more

u n i t s . In 1991, the survey was expanded t o inc lude bu i l d ings w i th

three o r more u n i t s . However, t h i s data i s no t necessar i ly

avai l a b l e f o r a l 1 CAS. S t a r t i n g i n 1996, data w a s co l l ec ted

annual 1 y each October . The mode1 shoul d have i n c l uded addi t i onal

var iab les f o r u n i t s i n bu i l d i ngs w i t h three o r more u n i t s .

Another problem was a change i n the boundary of a CMA/CA. A

few o f t h e study areas had one o r more CMA/CA boundary changes

over the study per iod. S t a t i s t i c s Canada r e a d i l y repor ts the

t o t a l popu la t ion f i g u r e f o r bo th the current and previous census

i n the Census o f Canada pub l i ca t ions . I f t he boundary was changed

f o r the cu r ren t c e n s u s , the previous census t o t a l populat ion i s

adjusted t o r e f l e c t the new boundary. However, adjusted data i s

not readi 1 y avai 1 ab1 e f o r p r i o r censuses - t h i s a l so appl i es t o

mover and dwe l l i ng data. Prec is ion of the r e s u l t s may be reduced

through overstated populat ion and dwel l ing growth ra tes .

One aspect not discussed i n t h i s study i s t h e impact o f ren t

cont ro l on changes i n r en t and vacancy ra tes . The general

e f f ec t s o f r e n t cont ro l are well-known and un ive rsa l . There i s a

vast amount o f l i t e r a t u r e on t h e t op i c . I n t h e beginning, ren t

cont ro l was t o be a temporary measure i n response t o sharp

increases i n r e n t . Over time, t he nature o f r e n t con t ro l ( from a

26

p o l i t i c a l p o i n t o f view) has focused on p ro tec t i ng low-income

households from "unreasonable r e n t increases" and as a

" s u b s t i t u t e f o r p u b l i c housing" (Ho 1992, pp. 1183-1184).

During t h e study per iod, a l 1 r e n t a l u n i t s were sub jec t t o

bo th r en t c o n t r o l and landlord- tenant l e g i s l a t i o n . Annual r en t

increases are capped a t a percentage l e v e l as determined by the

government. I n terms o f t h e model, t h i s has t he e f f e c t o f capping

increases i n r e n t as determined by t h e pr ice-adjustment

mechani sm. Rent con t r o l i n e f f e c t "breaks" t h i s mechani sm. Thus,

i t i s poss ib le t h a t the NVR i s understated f o r a l 1 areas. This

may exp la in w h y t he re i s l i t t l e v a r i a t i o n i n the NVR between

areas and why t h e NVR ra tes appear t o be low compared t o t h e

fi nd i ngs o f o the r authors.

6 .2 Future Research

Several d i r e c t i o n s o f f u t u r e research i n to t h e na tu ra l

vacancy r a t e a r e poss ib le . One p o s s i b i l i t y i s t o expand t h e area

o f study t o i n c l ude a l 1 CMA/CAs i n Canada, data permi tti ng.

Besides inc reas ing t h e sample s i z e , t h i s would pe rm i t researchers

t o compare and analyse the e f f e c t of d i f f e r e n t munic ipa l and

p rov i nc i a l regu l a t i ons on t h e r e n t a l apartment market.

An extension o f the above d i r e c t i o n i s the accommodation o f

r e n t con t r o l i n t he NVR model . Denton e t a l ( l 9 9 4 ) , i n a broad

study i n t o t he e f f e c t o f r e n t c o n t r o l on t he r e n t a l housing

market, hypothesized t h a t V e n t regu la t i ons are assoc ia ted w i t h

1 o w e r vacancy ra tes , other t h i ngs [be i ng] equal . " (p. 3 ) . Though

"scept ica l t l o f t h e r e s u l t s from t e s t i ng t h i s hypothesi s, Denton

e t a l p rov i ded a t heo re t i c a l and methodologi ca l s t a r t i ng po i n t

f o r t h e i n c l u s i o n o f ren t c o n t r o l i n NVR model.

More a t t e n t i o n could be focused on the du ra t i on o f the

vacancy o f a u n i t ra the r than t h e vacancy ra te . Th is would

introduce a more dynamic approach ta market behaviour. Read

( 1 988) attempted t o formulate a mode1 t h a t expl a i ns vacancy

durat ions i n r e l a t i o n t o adve r t i s i ng and the NVR. However, h i s

paper only presented the t heo re t i ca l framework t o permi t

empi r i ca l t e s t i ng . 6.3 Summary

The i n t e n t o f t h i s research was t o t e s t the NVR as a market

i nd i ca to r and t o evaluate the determinants of t he NVR. The study

complemented prev ious work on t h e NVR by Smith (1974) , Rosen and

S m i t h ( l 9 8 3 ) , Gabr ie l and Nothaft (1988) and others, and r e l i e d

on the empir ica l framework l a i d ou t by these authors. Due t o the

1 i m i t a t i o n s d i scussed prev i ousl y, t he prec i s i on o f t he resu l t s

has 1 i ke ly been reduced. Therefore, caut ion should be used when

i n te rp re t i ng t h e resu l t s .

This paper suggested t h a t t h e NVR i s p re fe rab le t o the

balanced market vacancy r a t e as a market i n d i c a t o r because i t

considers var ious socio-economic var iab les and government

regu la t ions . Based on these considerat ions, t h e NVR may be useful

i n eva luat i ng, modi f y i ng o r developi ng pol i cy. Therefore, the NVR

could be used i n conjunct ion w i t h the observed vacancy ra te , t o

determi ne i f a c e r t a i n p o l i c y o r group o f po l i c i e s have s a t i s f i e d

any goals o r c r i t e r i a . I n terms of urban planning, t h e NVR, when

appl i e d t o e i t h e r speci f i c areas of a municipal i t y o r t o speci f i c

dwelling types cou ld be usefu l i n encouraging and/or p ro tec t ing

those developments t h a t help t o balance the market.

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APPENDIX A

INDIVIDUAL STATISTICAL REPORTS

BARRIE CA STATIST ICAL REPORT

Constant - - ..

VR

Regression Statistics

Dependent variable

Analysis of Variai F

Std. Error Std. Emor ~ F T A of Beta b of b t (6) p-teve~

0.03390 0.01 573 2.15570 - - - - _ 0.07449

' -0.051 44 0.40778 -0.00114 0.00901 9.12618 0.90371

R = 0.0514: R~ = 0.0026: Adjusted R~ = -; Durbin-Watson = 1 .O546 - - - - - - -- - -- -- -- - - . -- -- - - - - - - F(1.6) = 0.0159 p c 0.9037: Std. Emx of Estimate = 0.021 1

PCR = Percent Change in Rent

ce Sum of Mean

- - - - - - - -- a - - - - A -

Residual 0.00267-- 6 0.00~Ck4- - - - - Total 0.00267

Descriptive Statistics ,

1 Vafid N Mean Sum Minimum Maximum

GUELPH CA STATlSTlCAL REPORT

L 1

PCR - - . . - -- - . VR

PCR VR

Analysis of Variance 1 Sumof Mean

8 0.032 - - - - - -. - - . - -. - . - - - -- 0.257 - 0.006

- 0.061

9 1 -389 1 2 . 5 ~ 0. l -~ - - 3.1 00 Range Variance Std. ûev Skewness Kurtosis

0.055 0.000 0.020 0.047 - - - - - -- - - -- -

-0.132 3.000 0.884 0.940 0.321 - - O. 121

Multiple Regression Resub

Constant - - -

VR

Regression Statistlcs

Dependent Vanable

- . .. -- - * - - - - Total 0100748

Std. Error Std. Emr BETA of Beta b of b t (6) p-level

- 0.05827 - - - - . - . - 0.02289 - - 2.54620 0.04371

-0.33038- - 0.38532 -0.01 077- 0.01256 -0.85742- 0.42413

R = 0.3304; R~ = 0.1092: Adjusted R' = -; Durbin-Watson = 1 S586 - - - - . -- Ç(1.6) = 0.7352 p c 0.424t; Std. Enor of ~stirnate = 0.0333


Reg ression Squares df Squares F p-lever

0.00082 1 0.00082 0.7351 7 0.42413

Descriptive Statistics

PCR VR

PCR VR

Valid N Mean Sum Minimum Maximum 8 0.041 0.332 O. 009

- . - - -- - - . . - - - - - - . . - - - -- - - . 0.083 9 1.400 12.600 O. 1 O0 2.800

Range Variance Std. Dev Skewness Kurtosis - 0.075 0.001 0.033 0.496 -2.1 24

- - - -. - - - - - - - - -- - - - - - - -- 2.700 1.1 17 1 .O57 0.090 -1.621

IRegression Statistics IR = 0.6322: R~ = 0.3996; Adiusted R' = 0.2996: Durbin-Watson = 1.2442 1

Multiple Regression ResuCts

Constant - ---

VR

Std. Error Std. Enor BETA of Beta b ofb t (6) plevel

7.1 5760 1 -81 657 3.9401 7 0.00762 -- -. -- -. --A - --- -- -- - - - - - - -- --- - -

-0.6321 7 0.31632 -1.98575 0.993ô1 -1.99851 0.09262

Dependent Variable

F(1.6) = 3.9940 p c 0.0926; Std. Error of Estimate = 1.7022

PCR = Percent Change in Rent 1

Analysis of Variance

Regression Residual Total

1 ~escr i~ t ive Statistics

KINGSTON CA STATlSTlCAL REPORT

Sum of Mean Squares d f Squares F p-level

11.57326 1 11 -57326 3.99405 0.09262 - - - - * - . - - - -- . - -- -

1738576- - -- 6 2.89763 - - - - - -- - - - -- - - - - -

28.95902

PCR - - .

VR

PCR - .

VR

Valid N Mean Sum Minimum Maximum 8 0.037 0.299 0.01 3

- - - - - -- - - - - - - -. - -- -- - .- -. - - - - 0.065 9 1 .sr8 14.200 0.400 2.500

Ranae Variance Std. ûev Skewness Kurtosis - .- - 0.051

*- 0.000 - 0.020 -0.099 -1.831

-

2.100 0.562--- 0.750--- - - -0.649 -0.965

'~nalysis of Variance 1 Sumof Mean

Multiple Regression Resuîts I

Constant - - -- - - -

VR


Dependent Variable

Std. Enor Std. Enor BETA of 8eta b of b t (6) plevel

1

- - 0.06848 0.0 1065 6.42936 0.00067 - -- - - - - - - 4.79637 0.24691 -0.01 396' 0.00433 -3.22529 0.01802

R = 0.7964; R' = 0.6342: Adjusted R' = 0.5732; Durbin-Watson = 2.0877 . - - - - y - - - - - - - - - - - - -

F(1,6) = 10.4025 p c 0.0180: ~ t d r Enor of Estimate = 0.0146 J


Reg ression Residual Total

Squares d f Squares F p-level 0.02231 1 0.02231 10.40248 -- 0.01 802

-- - --- -.

- . 0.00129 6 0.00021 - - - - - - - - 0.02360---


PCR - - VR

Valid N Mean Sum Minimum Maximum 8 0.039 0.308 0.009 0.065

- - - . - - - - - - -- --- . - - - - - ---- 9 1.956 17.600 0.300 4.200

Range Variance Std. Dev Skewness Kurtosis L

PCR .

VR

- 0.056 0.001 0.022 -0.150 -1.595

- - - . - - - - - - - - -- - - - -. - - --A - -- - .- -. - - - - 3.900 1.770 1.331 0.263 9.895

KITCHENER CMA STATISTICAL REPORT

I~ul t in~e Reoression Resuits 1 Std. Enor Std. Enor

6-A of 6eta b of b t (6) p-ievel 4.88928 2.48467 1 .%778

- - - -- - -- - - -- - -"- -- -- - -- -- -- - O.OS5 - ---

4.16455 0.40568 -0.32930 0.80587 4.40862 0.697W

R = 0.1645; R' = 0.0271 : Adjusted R' = -.13Sl; Durbin-Watson = 0.931 1 - - - - - - - - - - - - - - - - - - - - - - -

F11.61 = 0.1669 D < 0.6970: Std. Enor of Estimate = 3.2334 - -

I ~ e ~ e n d e n t Variable ~PCR = Percent Change in Rent 1 - - - -

l~nalvsis of Variance 1 1 1 Sum of Mean 1

Regression Squares df Squares F p-ievel

1.74567 1 1.74567 0.1 6697 0.69700 - - - - - Residual

LONDON CMA STATISTICAL REPORT

- -- - - - &. - - - - - - - - - . - - - - -. . . 62,72936 6- ' 1 0 4 ~ 8 9 -

--. - - -- - - - - - - - - -- - - -- - - - -- - - -- - - - - -


Multiple Regression Resub I Std. Enor Std. Error

Total 64.47503 A

PCR . - - --

VR

PCR . - -

VR

Valid N Mean Sum Minimum Maximum 8 0.040 0.319 4.003 - -- --.- -- - -- - - -.-- 0.077 9 2.478 22.300 0 . 4 6 - - --- 4.400

Range Variance Std. ûev Skewness Kurtosis

. 0.079 -- - -. -- - - - - - 0.001 0.030 4.145 .6-1

1 - - - - - - - -- - - - -1.541 -- -

4.000 1.618 0.143- -1.676

Constant

Analysis of Variai F

BETA of Beta b of b (6) p-level 9.69369 1 .a6638 5.19384 0.00203

- - - - . -.


ice 1

Sum of Mean

--

R = 0.8227; R~ = 0.6768; Adjusted R' = 0.6230; Durbin-Watson = 2.0399 - - - - - - . - - - - - -

F(1,6) = 12.5639 p c 0.01 22; ~ t d &or of Ëstimate = 1.2194

Squares d f Squares F p-level 1 8.6821 9 1 18.68219 12.56395 0.01215

Dependent Variable ~PCR = Percent Change in Rent

tics ,

Valid N Mean Sum Minimum Maximum

- Residual Total

- - - - - - -- - - - - - - - . . . - - -

8.921 80- 6 1.48697 - - - - - - - -- - - - . . - - . - - - - - 27.60399-

- VR

- - - - - - -- - - - . - - - - - - - - - -

9 3.600 - - 32406- 2.100 5.800 Rame Variance Std. Dev Skewness Kurtosis

PCR - - -

VR

- O.Oô3 -- 0.000 0.020 -0.480 0.223

.-- - ----- ----- -- . -- - 3.700 - 1.125 1 .O61 0.834 1.699

PETERBOROUGH CA STATlSTlCAL REPORT

Multiple Regression Resuits I

I Std. Enor Std. Enor

I Regression Statistics R = 0.6279; R~ = 0.3943; Adjusted F f = 0.2934; Durbin-Watson = 1.9217 -- -- -- -- - - - - . -. . - - - - -- - -. - - --

IF(1.6) = 3.9065 D c 0.0955: Çld. Enor of Estimate = 0.0223 1 Constant

- -

VR

l~ependent Variable ~PCR = Percent Change in Rent I

BETA of üeta b of b t (6) p-level 0.07285 0.02081 3.501 07 0.01281

- - - - - - - - . --. - . - - -. - - - . - - - - . -- - . - . - - - - - -- - - - 6.62796 0.31772 4.01 119 O. 00566 -1 -97648 0.09549

Analysis of Variance 1 Sum of Mean

1 Descriptive Statistics 1

Regression - - - Residual

.

Total

Squares d f Squares F p-kvel 0.00195 1 0.001 95 3.90646 -- - - . - -- - - - - . - - - - - - - - - - - 0.09549

-

- - 0.00300 6 - - 0.00050 -

0 k 9 5 ‘ -

ST-CATHARINES-NIAGARA CMA STATlSTlCAL REPORT

PCR - - .

VR

PCR - -

VR

~ul t ip le~egres~on~ResuI ts 1 Std. Enor Std. Enor

valid N -

Mean Sum Minimum Maximum 8 -- - -- . - - - - - . - - -

0.035 -

0.278 - - - - - - -0.02 - - - - - 0.û68 9 3.256- - 29.300 1 .O00 5.400

Range Variance Std. Dev Skewness Kurtosis 0.071

- - - -. . - - . - - - 0.001 0.027 - -. - . - - - - - -- 0.101

* - - - -- -1.61 3 4.400 2.135 1.461 O. 168 -0.964

l~e~ress lon Statistia IR = 0.9572; R~ = 0.9163; Adjusted R' = 0.9024; Durbin-Watson = 1.4167 - . . . . - - - - I

Constant

VR

BETA of Beta b of b t (6) p-levei

- - - - 9.451 95 0.77081 12.26235 - - . - . - - -

0.00002

-0.95724 0.11811 -1.51472 O. 18689 -0.81050- -- 0.00019

nalysis of Variance 1 Sumof Mean

Dependent Variable

F(1.6) = 65.6912 p c 0.0002; Std. Error of Estimate = 0.8931 !


Reg ression Residual

. -

Total

Squares d f Squares F plevel 52.40081 1 52.40081 65.691 18 0.00019

- - -. - -.

- - 4.78610- - - 6 -- 0.79768- a -

. . -.

57.18691-


PCR VR

PCR -

VR

Valid N Mean Sum Minimum Maximum 8

- - - - - - -. - 0.038 -- -

0.300 --- - 0.001 - - - - - - - 0.075

9 - 3.456- 31.100 0.900 5 . 8 ~ Range Variance Std. Dev Skewness Kurtosis

0.074 0.001 0.029 0.085 - - -1.974 -

4.900 3.703 1.924-- -0.180- -1 -81 O

Multiple Regression Results I ~ t d . Error Std. Enor

Constant - -

VR


BETA of Beta b of b t (6) p-level

0.08534 4.50660 0.00408 - * -

0.01 894 - -- - - .- - - - - -- - -- -

-0.74627 0.271 75 4-01 51 3 0.00551 -2.74616 0.03346


Dependent Variable

R = 0.7463; R' = 0.5569; Adjusted* = 0.4831: Duibin-Watson = 1 2471 - - - -- - - - - - -- - - -- - -- - - - - - - - - - - - - F(1.6)=7.5414 p < 0.0335; Std. Emr of Estimate = 0.031 1-

PCR = Perœnt Chanpe in Rent

DescriptiveStatistics - -

1 Valid N Mean Sum Minimum Maximum

Rwression Squares d f Squares F p-level

O. 00727 1 0.00727 7.54140 0.03346

WINDSOR CMA STATISTICAL REPORT

1 PCR

Range Variance Std. Dev Skewness Kurtosis

0.1 29 0.002 0.043 0.795 -0.037

Multiple Regression Resuits

' ~ n a l ~ s i s of Variance 1 Sumof Mean

Constant

VR

-Regression Statistics

Dependent Variable

Std. Enor Std. Enor 8ETA of &ta b of b t (6) plevel

7.1 8787 3.56821 2.01442 A - - - - - - . . -

0.04060

-0.37007- 0.37927- - -1 -53366 1.571 77 -0.97575- 0.36687 - - -

R = 0.3701; R~ = 0.1369; Adjusted R~ = -0.0069: ~ u r b i n - ~ a t s i = 1.6835 - - - - . . - . - - - - .

F(1.6) = 0.9521 p < 0.3669; Std. Ermr of Estimate = 3.071 5 4


Rearession Squares d f Squares F plevel

8.98208 1 8.98208 0.95209 0.36687

?


PCR -

VR

Valid N Mean Sum Minimum Maximum 8 0,039 0.310 0.014 0.103

. - - - - - -- - - s_l oo -- --- - 9 2.01 1 0:800- 3.000

Range Variance Std. Dev Skewness Kurtosis PCR VR

- J

0.089 0.001 0.031 1.625 2.232 ---. - -- --- ----- -

2.200 0.684 0.827 -0.205 -1.454

APPENOIX 6

POOLE0 DATA STATlSTlCAL REPORT

Constant - - -

VR - ---

Barrie CA

Guelph CA - - - - - . - --

Hamilton CMA - - -

Kingston CA

Kitchener CMA

London CG - -

Peterborough CA -. .

st.~atharines CMA

Sudbury CMA

Multiple Reglession Resub 1

r

F F . r F -

1 Regression statistio

Std. Enor Std. Enor BETA of Bcta b of b t (69) plevel

- - --- - - - -- . - O.il6538 0.00938 6.96570 . - - - - - - - - - - - - - - - - - - - - - .- - - - 0 . m

- --

-0.68924 0.1 1692 9.01 233 0.00209 -5.89478 - 0.0000(1 -- -- - --A-- --- -- - -- - -- - - -- - - - . - -- -

-0.160% 0.13149 -0.01426 0.01 170 -1.21961 0.22673 - - - - - &. A -. - -- - - - - - - - -- -- -- -- - - - -. - - - - - - - - - - - - - - - - . - -

-0.05244 0.13142 -0.00467 0.01 469 -0.39904 0.691 09 - - - - - -. - - --- -- -

4.07630 0.1 31 07 -0.00679 0.01 166 -0.58214 0.56237 - - - ----- -

-0.00459 - - - - -

0.13066 -0.00041 0.01 162 -0.0351 3 0.97200 -- -- - - - - -- - - - - - - -- - - -- - -- - -- - - - - - - - 0.09282 0.1 31 36 0.00826 0.01 168

- - - - - - - - - - - - - * 0.70657 0.48221

0.1 5623 0.1 3614 0.01 390 0.0121 1 1.14761- - 0.%09 - - - A - - - - - - - -. - - - -- -- - -- - - - . - - - - - - -. - .

-- 0.1 2762 0.13387 0.01 135 0.01 1@ - - - - - . - - - - --- - - - A - - - -. . - . - -- 0.95331 0.34376

0 . 2 0 8 g - -

O. 13597 0.01 855 0.01209 1.53338- -

--LA----.---- - - - - - -

0.12976

O. 1 3622 0.13:52 0.01212 0.01 170 1 .O3573 0.30%

Z = 0.5878: R' = 0.3455; Adjusted R' = 0.2507; Durttin-Watson = 1.7130 - -- - - . -- - - - - -- -

:(10.69) = 36431 p c 0.0006; Std. ~ k r of Estirnate = 0.0232 - -

CR = Percent Change in Rent


1 1 aua ares d f Sauares F wlevel 1 Regression 1 0.01968 10 0.00197 3.64307 0.0061 81

- Correlation Matrix 1 Variable I' VR PCR 1

I Hamilton CMA

Kingston CA I I Kitchener CMA

London CMA

Sudbury CMA l+l

Please note: Correlation between al1

durnmy variables was -0.1 1.

Descriptive Statistics 1 ValidN Mean Sum Minimum Maximum

PCR - -.

VR

PCR - - . -

VR

80 0.03759 3.60680 -0.00694 . --- . - -- - - -- ---- - - - -- - -

0.12180

80 2.56250 205.00000 0.1 0000 5.-kOilC

Range Variance Std. Dev Skewness Kurtosis

O. 1 2873 0.00721 0.02685 0.59215 -0.02642 -- ---- ---- -

5.80000 2.25250 1.50083 0.44663 -0.53436

APPENDIX C

NATURAL VACANCY RATE STATlSTlCAL REPORT

NATURAL VACANCY RATE STATlSTlCAL REPORT

' ~ u l t i ~ l e Regression Result. 1 ~ t d . Enor Std. Error

'constant

RNT -

cSH - -

CPOP

MOB

BETA of Beta b ofb t (4) p-kvel

- --- 12.5309 10.9920 1.1400 0.3179

- - - - A . - - - - *

4.3376 0.6336 4.0093 0.01 74 -0.5327 0.62î4 --- -- - - - -1 -3050 -

0.9907 O. 0000 0.0000 -1.31 73 0.2581 . - - - - - - - -- ---- - - -

2.9470~- ' 1.6874 0.0021 0.0012 1.7465 O. 1557 - - - -- - - -- - - A A- -- - - - - -- - - -- - - -- - - - - -

-1 -9340 1.3198 -0.0007 0.0005 -1.4654 0.2167 - - - - -- -- - - -- -- ----- -- ---

-0.3813 0.4363 46.71 37 53.451 1 -0.8740 0.431 5 -- -


Dependent Variable

- - - - - - -

R = 0.8096; R* = 0.6554: Adjusteci R' = 0248; Durbin-Watson = 1.0396 - -- - - - - -- - - - - - - - - - - . - -

F(5.4) = 1 S221 p < 0.3525: Std. Enor of Estimate = 0.7714 1

W R = Natural Vacancv Rate

Analysis of Variance 1 Sumof Mean

l~orrelation Matrix 1

Regression - -

Residual - - - _ Total

\variable 1 R M PS cSH cPOP MOB NVR 1

Squares d f Squares F pkvel 4.5285 5 0.9057 1 S221 0.3525

, - -. . - - - - - - - - - - - . - -- - - - - - - -- - -- -- - - 2.3801 4 0.5950 _ _ _ - - _ - - - _.- -- - - - _ _ _ ---, 6.9085

1 Descriotive Statktics 1

RNT

PS

cSH - . --

cPOP

MOB - - - -

NVR

RNT PS cSH cPOP MO5 NVR

1-00 -0.66 -0.54 -0.27 -0.19 - - - - - - - - - -- - - - - A - - - - - - ---.. *-

-0.49 -- -

- - -0.66 - -.-. - 1 .O0 009 0.74 - - - - 4.07 -- -

0.15

. - -0.54

-.-- 089-

- . - - -- - - - 1%-- - - 0.93 0.20

- - - 0.10

-0.27 0.74 0.93 1 .O0 - - - - - - - - - - - 0.27 - - --

-0.17

. - - 4-19 -- -- -- -0.07

- - - 0:20- - - - 0.27 1 .O0 -0.16 - - - . - - - - - - - -

-0.49 0.15 011 O -0.17 -0.16 1 .O0

RNT - - - - FS c S H cPOP MOB NVR

Valid N Mean SUIG Minimum Maximum 1

- - . - - -. - - -- 10 3636.500--36365.000- - -- . - - - - ~ll6l.OOO -- - 7175:~~ -

10- 0.034 0.344 0.024 0.045 Ranae Vananœ Std. Dev Skewness Kurtosis

NAME:

PLACE OF BIRTH:

YEAR OF BIRTH:

EDUCATION:

Adam Mark Szymczak

Toronto, Ontario, Canada

St. John's College, Brantford, Ontario 1981-1986

University of Toronto, Toronto, Ontario 1 986-1 990 B.A. Emnomics 8 Geography

University of Waterloo, Waterloo, Ontario 1990 Post-Degree Studies

University of Windsor, Windsor, Ontario 1994-1 998 MA. Geography (Urban Planning)

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