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UBC Theses and Dissertations

Housing demand and taxation Heikkila, Eric John 1986

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HOUSING  DEMAND  AND  TAXATION  by  ERIC  JOHN  HEIKKILA  B.A., Lakehead M.A., Dalhousie  THESIS THE  SUBMITTED  IN  REQUIREMENTS DOCTOR  University University  PARTIAL FOR  OF  FULFILMENT  THE DEGREE  OF  PHILOSOPHY  in THE  We  F A C U L T Y OF  GRADUATE  Department  Of  accept to  THE  this  the  thesis  OF  October  ©  Eric  Economics  required  UNIVERSITY  STUDIES  as  conforming  standard  BRITISH  COLUMBIA  1986  John H e i k k i l a ,  1986  In  presenting  requirements  for  Columbia,  I  available  for  permission  this an  thesis advanced  agree  for  and  study.  I  granted  this  thesis  my  written  without  Department  of  by  October  the It for  Head is  6  1986  this  of  my  Columbia  thesis  gain  the  of  British  it  freely  agree for  Department  understood  permission.  make  further  of  financial  Economics  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  Date:  copying  of  University  reference  representatives.  allowed  the  shall  or  of  at  Library  may  publication  degree  fulfilment  the  purposes her  p a r t i a l  that  extensive  be  in  that  that  scholarly  or  by  copying  shall  not  his or be  i i  Abstract This develop with  dissertation  and  test  tenure model  tax  changes. The  However,  been this  efficiency The  used  in  effect  model  of  confirm  evaluate  This  the  context  of  equity  and  the  thesis  demand  is  (2)  the  to  United  proposal  of  tax  and  on  complete how  housing-related  income  States  to  demonstrate  introduction  Similar  a  empirical  tested  Toronto  mortage  deductions  Great  both  Britain.  equity  v i t a l  empirically  metropolitan costs  and  component  of  demand  result  for  that  the  are  not the  effectively  residential  immobility  due  sum  is  not It  proposed  deadweight  in  is  housing.  e f f i c i e n c y of  are  lump  the  was  transactions  are  p a r t i c u l a r l y  subsidies  model  from  that  subsidies  summarized  and  demand  alternative  Canada.  rejects  housing  (1)  and  using  area.  other  These  barriers  the  a  to  households'  process.  key  The  here  the  mobility  decision-making  claimed,  costs,  in  households  interest  of  objectives:  grounds.  residential  to  to  primary  model  moving  evaluated  housing  results  this  and  d e d u c t i b i l i t y in  long  sample  be  proposal  interest have  can  two  empirically a  choice  this  has  as  impinges It  attributable as  run.  transformed And  important  changes.  severe  short  high.  also  tax  loss  only  has  The  into  there  to  no  sum  the  on  the  shown  in  mortgage  sometimes  reason  lump is  is  in  is  been that  grants  when  deadweight  loss  therefore  be  grants.  main  findings  of  as  follows:  (1)  this the  thesis  housing  may  demand  decision  is  best  understood  when  e x p l i c i t l y , into  and  barriers (2) t h e  consideration  implications  of  to  presence  when  proposed  residential of  mobility  these  calculating housing-related  barriers  the tax  short  are  modelled  must  be  run  changes.  taken  welfare  Table  of  Contents  Abstract  i i  List  of  Tables  List  of  Figures  v i i i  Acknowledgement  ix  I .  II.  III.  v i i  Introduction  1  A.  Overview  B.  Housing  C.  Residential  D.  Chapter  Modelling  1 Demand  and  Mortgage  Interest  Deductibility  Mobility  5  Synopses  Housing  A.  The  Basic  B.  Alternative  C.  Moving  Costs  D.  Tenure  Choice  8  Demand  11  Model  Econometric  11  Representations and and  the  of  Demand  the  Moving  for  Demand  Costs  Housing  for  Housing  Specification  A.  General  Formulation  B.  Linking  Tenure  Linking  to  Specifying  E.  Logit  F.  Likelihood  vs  36 Demand  to  Preference 39  Functional  Form  Probit Function  26  Preference  Parameters D.  18  33  Probabilities  Conditional  13  33  Parameters C.  2  40 44  Specification  50  V  G.  IV.  V.  S p e c i f i c a t i o n  Data  and  of  Base  Model  58  V a r i a b l e s  62  A.  I n t r o d u c t i o n  62  B.  The  65  C.  Measuring  Data Accomodation  1.  Hedonic  2.  Owner  D.  The  P r i c e  E.  D e f i n i n g  E s t i m a t i o n  of  housing  versus  q u a n t i t y  r e n t a l  67  accomodation  Accomodation  and  84  R e s u l t s  of  the  B.  N o n l i n e a r  C.  Demographic  88  Basic  Model  88  E s t i m a t i o n  91  V a r i a b l e s  1.  Demographic  2.  I n i t i a l  3.  Demographic  91  s c a l i n g  e s t i m a t i o n  and  t r a n s l a t i n g  attempts  v a r i a b l e s  and  tenure  c h o i c e  96 99  1.  D i s u t i l i t y  2.  E x p e n d i t u r e  3.  R e n t a l  4.  Red  the  91 93  R e s u l t s  Is  72 77  E x p e n d i t u r e  Summary  E.  of  o c c u p i e d  A.  D.  index  67  of  R e l o c a t i o n  and  versus  Owned  H o u s e — B l u e  F u l l  Model  1.  Tenure  2.  C o n d i t i o n a l  3.  C o n c l u d i n g  P r i c e  ( K )  99  E l a s t i c i t i e s  Accomodation  House  (a)  111  Alone  Share Remarks  Equations  109 110  Necessary?  Choice  (v)  105  111 Alone  114 114  vi  VI.  Evaluating A.  Mortgage  B.  Efficiency  C.  D.  VII.  Tax  Reforms:  Interest  An  and  Example  Property  Tax  Equivalent  Gain  of  a  Tax  2.  Deadweight  Loss  of  a  Price  3.  Empirical  Evidence  Distributional Equivalent  2.  Social  3.  Empirical  and  A.  Summary  B.  Ideas  for  118  122  Subsidy  126  Efficiency  130 134  Expenditure  Welfare  Assessment  on  Reform  Evaluation  1.  Summary  Deductibility  122  1.  An  118  and  Evidence of  Agenda  Price  for  134  Proportional  Social  on  Welfare  138  Homeowners  143  Aggregate  Subsidies  Future  for  Research  Gain  137  147 147  Future  Research  148  Bibliography  152  Appendix  A  158  Appendix  B  161  Appendix  C  163  Appendix  D  165  Appendix  E  168  Appendix  F  170  v i i  List  I.  II.  Estimation  Crosstabulations Selected  III.  IV.  Maximum  VII.  Transactions  Costs  Income  Comparative  VIII.  IX.  X.  XI.  Maximum  Effect  of  Price  of  Loss  Price  Estimates  as  Mean  71  and  Parameter  for  and  on  the  Full  of  on  Half  Model  for  Prototypes and  Logit  Model  Values  104  Only  113  Choice  131  Estimates  132  Welfare  versus  for  102  Tenure  Subsidy  Social  100  Residential  Expenditure  Tenure  Price  Subsidy  of  97  Household  Price  to  Two  Model  Mobility  Characteristics  Subsidy  Due  Regressions  Proportion  Estimates  Effects  of  a  Eight  Comparative  Sets  Hedonic  Attributes  Household at  Tables  Residential  for  Likelihood  Deadweight  Effect  of  Likelihood  Probabilities  VI.  for  Demographic  Household V.  Results  of  Full  the  Subsidy  139  142  Linear 167  v i i i  List  1.  Different  Measures  2.  Discontinuities  3.  Staying  4.  Effect  of  Differing  5.  Effect  of  Kappa  6.  Owning  versus  Renting  7.  Owning  versus  Renting  8.  Structure  9.  Theta  in  of  of  10.  Choosing  the  11.  Deadweight  12.  Relationship  14  Demand  19  Moving  21  of  Kappa  on  S  24  25  27  versus  Staying  28  Decision  Demand  of  Costs  Discontinuities  Correct  Loss  Transactions  Values  Tenure  Shifting  Figures  Housing  Preferred to  on  of  a  Between  46  Curve  76  Measure  Price  c()  of  Equivalent  Subsidy  and  f()  Gain  124  127  159  ix  Acknowledgement Peter Chinloy provided valuable encouragement during the c r i t i c a l e a r l y stages. T e r r y Wales assumed the t h a n k l e s s task of supervising the thesis after i t w a s a l r e a d y w e l l u n d e r w a y ; I am p a r t i c u l a r l y grateful to him for that. John Cragg provided cheerful and c o n s t r u c t i v e a d v i c e w h i c h f o r c e d me t o t h i n k m o r e deeply about the e m p i r i c a l model. Dennis Capozza was always p r e p a r e d t o l i s t e n a n d a d v i s e on a w i d e r a n g e o f m a t t e r s . Numerous o t h e r f a c u l t y members and f e l l o w g r a d u a t e s t u d e n t s there when needed. Many s m a l l a c t s of k i n d n e s s h e l p e d t o t h i s four-year burden s i g n i f i c a n t l y . Ann M c A f e e , Ted Droettboom, Vancouver C i t y H a l l bent over of absense. My w i f e C h e u n g S i u F o n g patiently for countless  Hugh Creighton, and others at b a c k w a r d s t o a c c o m o d a t e my l e a v e s  and c h i l d r e n , Aarne hours.  Above a l l , I must t h a n k my M e n g K o n g a n d I s a b e l l e , a n d my h o p e t h a t my s u c c e s s f u l c o m p l e t h e i r profound and unwavering  were ease  and  Laila,  waited  b r o t h e r - and s i s t e r - i n - l a w Cheung w i f e ' s m o t h e r Wong M u i Y u . I only t i o n i n some s m a l l way j u s t i f i e s support.  1  I.  Introduction  A.  Overview  This develop  dissertation  and  with  tenure  this  model  tax  test  reforms.  extends  and  economics The Laidler  be In  f i r s t  subsidy and  households selected The and  is  and  Wise  authors stock  used  is  to  model  of two  these  objectives:  of  costs,  evaluate  housing  and  (2)  to  (1)  to  demand  complete  demonstrate  alternative housing goals,  d i s t i n c t  Aaron  to  they  the  work  streams  (1984). express  adjustment  work  Rosen  these used  income  expenditures stream  of by  Weinburg, The  in  how  related  presented  the  here  housing  current  in  demand  and  moving  implications  of  payments  is  a  rooted  the  and  other  income.  Mayo  on  moving  developed  may  costs,  Hanushek  (1981),  consumption costs  in  a  allow  t r a d i t i o n of  models  housing  King of  which  focuses  the  of  model  subsidy  taxable  Friedman,  where  and  the  provisions  from  period  process,  This  t r a d i t i o n  developed  analyze  interest  work  the  (1979),  literature  housing  in  authors  to  tax  mortgage  represented  (1978),  of  by  owner-occupiers.  deduct  second  (1972),  Each  which  housing  adjustment.  represented  B r i t i s h  to  best  Quigley  primary  literature.  demand  American  moving  pursuit  (1980,1981,1983).  price  and  synthesizes  (1969),  housing  two  empirically a  choice can  has  in  and  and  Venti  by  these  terms  impede  that  of  a  2  By aspects in  a  merging  these  of  are  more  each  determining better price  subsidy  detail  earlier  which  of  factors  mobility.  And  welfare  sections  work  authors.  provides  model  and  the  beneficial  moving  housing  are  costs  results  demand,  instrumental  this  in  turn  in  leads  to  efficiency effects  of  a  owner-occupiers.  two  this  robust  the  streams,  Incorporating  demographic  of  to  next  how  and  household  estimates  The  of  when  separate  pooled.  r e a l i s t i c  particularly  two  a  of  builds They  brief  this  upon  are  chapter  and  discuss  extends  followed  by  synopsis  of  each  Mortgage  Interest  the  the  of  in  contributions  final  the  more  section,  remaining  chapters.  B.  Housing A  Demand  branch  of  closely  related  classic  paper  federal  income  United  interest  tax  the  subsidies.  how  and  income,  Aaron  the  to  which  (1972) tax  resulting  L a i d l e r ' s  associated  allowed  to  local  they  they  with  (1969) 'hidden'  changes  would in  to  have  tax  In  taxes  the  from to  claim  the  homeownership.  data,  associated  data  is  mortgage  required  from  demand  burden  subsidy  not  derive  micro  deduct  property  are  housing  used  which  homeowner-occupiers.  and  excess  Deductibility  literature  with  losses  yet  aggregate  the  began  are  state  aggregate  eliminating  analyze  welfare  subsidies  income  with  taxation  study  homeowners  rental  estimated  housing  this  the  taxable  Working  that  to  payments  household imputed  the  on  States,  and  Laidler with  examine on  these  the  impact  homeowners  l i a b i l i t i e s  would  and  to  vary  3  with  income  examined  levels.  the  Neither  interaction  Laidler  between  (1969)  rental  nor  and  Aaron  (1972)  homeownership  markets. It  remained  analyzing are  free  housing burden Rosen  household to  switch  demanded. among  gross  examines  decisions  the  within  Three  a  papers  present  the  welfare  costs  most  occupiers. an  for  In  econometric Kingdom.  choice  and  the  M.A.  index  function  of  with of  of  in  gains  tax  on  change  households  the  quantity  distribution  Like  Lee  and  of  Trost  conditional  of  excess (1978),  demand  (1980,1981,1983) approach  these  these  tax  to  demand model  demand  taken  date  in  subsidies  papers,  f i r s t  the and  King  and in  together  measuring for  develops  choice  which  both  are  the  owner-  (1980)  tenure  decisions  the  two  subsequent  losses imputed  (King,1981),  dissertation  the  and  distributions  (King,  to  for  in  the  the  tenure  e x p l i c i t l y  preferences.  model  a  where  as  framework  framework.  King  f i r s t  set  These  recognizes  choice  conditional  occupation.  several  tenure  the  of  in  groups.  by  introduction  This  income  is  distribution  changes  examines  then  His  this  tax  He  housing  uses  a  well  of  He  develop  as  model  one  to  tenures  likelihood  the  from  welfare  to  sophisticated  derived  inequality  (1979)  responses  associated  United  the  Rosen  or  are  papers  associated rental  income  assessed  d i r e c t l y  with  a  evaluate  the  from  either  through  to  by  owneran  social  1983). differs  from  these  earlier  respects.  Most  importantly,  the  e x p l i c i t l y  that  moving  w i l l  costs  model  contributions developed  persuade  many  here  4  households prices  to  and  The  models  discussed  adjust  effortlessly and  evidence  stationary  despite  from  their one  above  level  period  expenditures.  suggests  that  implicitly  of to  housing the  Whereas  in  demographic  whether  does  to  t r a d i t i o n a l economic  look  much It  us  a  But  accommodation is  useful  better more  results  relative  in  a  deadweight  household  to  consume.  i t s e l f  that  representation  importantly, in  a  greatly  loss  of  reduced  resulting  model  the  are  the  empirical  the  chief  only  as  i t  into  short  then  determines  here  decision  introduction  changing  the  and  feature of  of  presented  housing  this  that  face  model,  variables  estimate  from  the  relocates,  the  introducing  in  this  the  how  assume  variables  of  how  in  consumption  next  determinants i t  changes  income.  households  prices  remain  gives  is  the  made.  model  run  of  the  price  subsidy. When less  the  l i k e l y  housing  to  deadweight This  do  likely housing  loss  the  for  to to  be  moving  When  this  into  with  of  is  a f f a i r s  longer  the  run,  results  influenced  consume.  by  happens, sum  lump  and to  price  the  sum to  level  price  subsidies  only  there  over  households  subsidy.  here  subsidy  And  are  of  is  are no  grants. hold  more  subsidies  their  grants.  the  presented the  high,  readjust  l i k e l y  more  unrelated  is  to  lump  associated  reasons  move,  of  households  transformed  state  Over  relocate they  induce  consumption.  effectively  run.  d i s u t i l i t y  suggest  when  the  w i l l  However, that  deciding  short  once  they how  are  much  5  The  tenure  extension.  Instead  households (r)  move  any  given  in  this  may into  rental  period.  order  potential  u t i l i t y  to  Finally, Canadian  focus  markets, part  of  where  mortgage The  tax  rather  C.  Most  which  may  the  by  King  to  or  the  there  (s)  are  remain  play  an  and  tax  by  this  three; housing,  stationary important  in  part  model  of  with  is  and  restricted the  This  tax  and  this a  model  similar  out  the  In  American  Canada,  therefore,  is  the  is  set  in  research housing long  there  d e d u c t i b i l i t y for  tax  to  direct  rules  d e d u c t i b i l i t y has  systems.  the  household's  Rosen.  B r i t i s h  here, of  by  studies  the  a  indirect  application  property  removal  the  of  e x p l i c i t l y .  interest  been is  no  homeowners.  introduction  reform.  Mobility of  housing  e x p l i c i t l y .  The  standard  nothing  than  consumption  as  income.  some  In  somewhat  owner-occupied  or  tenure,  Earlier  King  1  into  comparison  both  empirical  and  more  tenures  variables  written  simulated  models  (1979)  be  respective  policy  move  each  mortgage  interest  than  (o)  direct  applied  Residential  Rosen  for  the  their  a  favored  been  possible  Demographic  context.  have  complicated  accommodation,  under  forms  forms  to  make  functions  translog  two  is  decision.  u t i l i t y  functional  decision  of  choose  move-stay  In  a  choice  a  a  demand,  (1980)  model  single  not of  these  housing  function models  those  incorporate  equation  log-linear cases  do  including  of  moving  demand  describing  is  by  costs  often  housing  housing  recognize  developed  prices  the  and  potential  for  6  disequilibrium movers  in  A  the  in  experiment  Housing  Allowance  impetus  for  by  low  a  These income  of  studies  and  a  analysis  to  estimate  actual  stock  but  cast  u t i l i t y the  housing  the  whether  estimated  Marshallian  on  decision  is  this  on  this  Wise same  the  interactively, focus  costs  recent  conducted  within  overwhelm  the  has  costs  served and  the as  housing  decision  housing  process.  Mayo  They  of  faced  a  disequilibrium  use  move;  probit  where  that  with  the  gap  between  (1981)  use  the  same  e x p l i c i t l y That  of  is  the  (1984) HADE  data  than  in  effectiveness  programs'  a  They  set.  desired  of  a  very  only  if  the  costs.  the  They  change  in  estimated  thorough  model  demand stage  various  demonstrate  incentives  move  consumption  comparing  They  two  set,  household  transactions  with  data  move.  housing a  of  households  surplus  from  terms  housing  by  present  conditional  HADE.  case  consumer  in  is,  incurring  resulting  rather  the  States,  Phoenix.  analyze  readjusting  d i s u t i l i t y  costs  and  and  from  determine  based  United  move-stay  and  probability  behavior.  the  and  the  monotonically  outweighs  Venti  moving  on  (1978)  the  2  on  focus  adjustment  moving  u t i l i t y  transactions  only  consumption.  maximizing in  including  (HADE) ,  Pittsburg  Friedman,  their  gain  in  increases  Weinburg,  studies  Quigley  of  and  by  in  Experiment  a l l  renters  terms  probability  market  conducted  Demand  number  Hanushek in  housing  sample.  unique  demand.  the  to  the  analysis move-stay  decision  procedure. rental that  increase  Their  subsidy  high  moving  housing  programs costs  7  consumption,  thereby  limiting  the  effectiveness  of  those  programs. The spirit  research  of  example, thus,  these the  choice  move-stay  own-rent  in  the  aspects,  move/rent,  from a l l  the  therefore  The  Toronto  tenures  and  of  d i f f e r s  is  not  preceding yielding  in  The  to  HADE  This  trimodal  very  much  of  studies  and  alone; a  bimodal  King  decision;  the  For  model  the  research  in  ways.  renters  with  (1979)  section.  is  number  contrasts  Rosen  the  a  confined  This by  thesis  (1980),  as  integrates move/own,  stay.  Similarly, restricted.  this  introduced.  modelled  thus  or  but  here  is  for  decision.  decision  discussed both  authors,  analysis  tenure  bimodal  undertaken  the  empirical  data  used  Census income  wider  focus  here  3  for  comprise  Metropolitan groups.  this  The  a  Area  research sample  (CMA),  resulting  a p p l i c a b i l i t y than  those  is  of  less  households  representing  estimates  from  the  are  HADE  studies. Finally, the  welfare,  subsidies HADE  to  studies,  tenure  this  model  tenure,  of  housing  mobility,  owner-occupiers. which  effects)  of  examine rental  the  and  demand  is  applied  to  examine  efficiency  impacts  of  price  Such  was  efficacy  subsidies.  not  the  (but  intention  not  the  of  welfare  the or  8  D.  Chapter This  t h e s i s comprises  formulates given it  the  period  may  seven c h a p t e r s .  t h e o r e t i c a l model of  the  household  faces  move i n t o o w n e r s h i p or  remain  stationary.  indirect net  Synopses  'subutility'  income, and  option  Each of  derives  the  Chapter  three  basic  two  demand.  In  any  or  tenures;  options  r e n t a l accommodation  index d e f i n e d  given  greatest  three  these options  demographic  from w h i c h ;  housing  Chapter  over  status.  it  is associated the  The  or  may  with  household's p r i c e s ,  household chooses  p r i c e s , income, and  utility.  specifies a the  likelihood  f u n c t i o n which i s  concerned with  housing  s e r v i c e s demanded c o n d i t i o n a l upon t e n u r e c h o i c e .  expenditure  t e n u r e d e c i s i o n and  modelled within  the  four  describes  the  estimating  the  model's parameter  relatively  new  data  and  the  framework of a  quantity  of Both  linear  system.  Chapter  Life  that  moving c o s t s ; i t  jointly  d e c i s i o n s are  an  Survey. housing  s e t , the  It contains  data  and  v a r i a b l e s used  values.  I t employs  in  a  S o c i a l Change i n C a n a d a ; Q u a l i t y  panel  v a r i a b l e s w h i c h may  data be  on  many p e r t i n e n t  of  financial  r e a d i l y incorporated  into  our  model. The chapter  estimation five.  estimation the  confirm  model.  influence  The  And on  the  p r o c e d u r e s and  r e s u l t s are  r e s u l t s from t h e the  importance  of  maximum  in  likelihood  i n c l u d i n g moving c o s t s  demographic v a r i a b l e s are likelihood  described  in  shown t o have a m a j o r  of a move.  T h e s e r e s u l t s have t h e i r  counterpart  in chapter  s i x , which  9  applies  the  subsidies are  no  to  moving  deadweight household almost  model's  findings  homeowners. costs,  loss  and  welfare.  negligible  the  to  the  evaluation  Using  the  standard  subsidy  in  a  In  contrast,  short  less  run  results  equitable the  impact,  in  of  model,  distribution  to  tax  where  there  substantial  transactions due  income  the  of  model  paucity  shows  an  of  movers. Chapter p o s s i b i l i t i e s  seven for  summarizes further  the  research  research.  findings  and  outlines  10  NOTES  For a good ( 1 9 8 1 ).  review  of  TO  CHAPTER  these  ONE  standard  models,  see  Mayo  The H o u s i n g A l l o w a n c e Demand E x p e r i m e n t was f u n d e d by the U n i t e d S t a t e s Department of Housing and Urban Development. M u c h of t h e HADE r e s e a r c h r e p o r t e d on h e r e was conducted under the a u s p i c e s of Abt A s s o c i a t e s Inc. The d a t a u s e d i n t h i s t h e s i s was g e n e r a t e d by t h e S o c i a l Change i n C a n a d a P r o j e c t d i r e c t e d b y Tom A t k i n s o n , Bernard B l i s h e n , M i c h a e l O r n s t e i n , and H. Michael Stevenson of York U n i v e r s i t y , Toronto. The r e s e a r c h was s u p p o r t e d by the S o c i a l S c i e n c e s and H u m a n i t i e s Research C o u n c i l of Canada (Grant # S75-0332). Responsibility for the i n t e r p r e t a t i o n s p r e s e n t e d here i s mine a l o n e .  II.  Modelling  A.  The  Housing  Basic  At  the  housing  Demand  Model  beginning  options,  of  each  denoted  by  period  subscript  ownership  accommodation  (j=o),  (j=r),  remain  present  or  in  selects  that  option  u t i l i t y  over  the  In  making  factors, of  its  which  move  It  may  into  rental  location  (j=s).  w i l l  period. the  attributes,  attachment.  household j .  expects  decision,  demographic  residential  i t  forthcoming  this  a  three  move  basic  into  accommodation The  yield  household  the  greatest  reviews  economic  1  household and  Price  has  intangible  (p  ),  considerations  expenditure  levels  (e  j on  housing  with  each  and  other  tenure  Demographic household  (j=o,r,s)  attributes  head  Three  consumables,  and  (d)  family  indirect  are  j  and  the  moving  main  include  age  costs  economic and  associated factors.  marital  status  of  size.  subutility  indexes  (V  )  correspond  to  the  j three  basic  relocation given  tenure  choices.  (m=o,r),  the  For  the  indirect  two  options  u t i l i t y  for  which  household  entail h  2  by  h V  h =  m  V  (p m  ,e m  )  h =  max  m  U(x x  ,x  h  )  m  -  to  p  K  (d)  (2.1)  c h  subject  x m m  )  h +x  h <  c  e m  is  12  h where  x  is  the quantity  of  accommodation  services  consumed  by  m h household  h  in  tenure  m,  x  is  the quantity  of  other  goods  c consumed,  and U  is  the direct  u t i l i t y  function  net  of  relocation. The  expression  residential developed is  obtained  by  setting  of  the d i s u t i l i t y  The s t a n d a r d  Lee and Trost  here,  d i s u t i l i t y  gives  relocation.  by  described  «(d)  (1978),  «(d)  =  0  as  3  a  Rosen  term  function  tenure  In  «(d)  of  of  (1979),  f o r a l l h.  the transactions  a move  model  associated  with  choice  and King  the  (1980)  model  expresses  household  as  the  total  demographic  characteristics". If  the household  does  n o t move,  then  i t s  housing  h consumption  is  fixed  at  x  ,  and the  5  remainder  of  i t s  s expenditures indirect  for  u t i l i t y  the period  go  to  associated  with  other  the stay  h V s  The of  = V (p ,e s s s  indirect these  indirect  is  defined  ,(e - p x )] s s s s  function  subutility  for  the by  (2.2)  the household  indexes.  h = V(p,e)  option  Thus,  h = U[x  u t i l i t y  h V  )  consumables.  That  is  the  supremum  i s ,  h = max  [V  ,V  ,V  ]  (2.3)  13  This Muth's  view  (1974).  exogenous expected tenure  B.  of In  shock price  and  Alternative  terms  the  of  express  which  V  The  TC  =  in  e  These  +  of  )  -  m  of  the  e  the  Moving moving  /c(d),  costs  these  ,V m  of  sought.  are  measured  one  monetary  that  in  could TC(d).  transactions  6  (2.4a)  measures  expenditure  (p m  two  length  expenditures,  the  so  But  Costs  foregone as  to  an  expected  Alternatively,  defined  is  changes.  accommodation  of  to  over  move  /c = V ( p , e ) m m m  between  ,V m  be  to  kinship  can  also  be  function;  -K)  (2.4b)  m  representations  are  i l l u s t r a t e d  in  figures  1a  1b.  world  But  -TC) m  alternative  U*  This  paths of  terms  TC(d)  terms  (p m  and  ,e m  in  certain  demographic  /c(d).  equivalent  relationship  expressed  on  a  decision  described,  u t i l i t y ,  let  (p  largely  just  bears  the  quantity  costs  are  m  model,  Representations  foregone moving  demand  expenditure  the  model  Specifically, costs  his  based  determine  In  housing  denotes  without  the  moving  corresponds in  our  model,  to  maximum  level  of  costs,  given  prices  point  because  (1), of  the  u t i l i t y p*  mover's  transactions  attainable and  in  a  expenditure  choice,  in  figure  d i s u t i l i t i e s ,  e*. 1a.  14 Figure 1 D i f f e r e n t Measures of T r a n s a c t i o n s  Costs  15  the  mover's  choice  yields  a  u t i l i t y  of  only  V  *  = U * - K .  U*-K  attain  with  is  m also  the  maximum  expenditures  of  represented The 1a  has  by  u t i l i t y e*-TC  its  in  point  u t i l i t y  movers'  and  Engel  its  counterpart,  a  household  world  with  expenditure in  curve,  1b. X  no  7  level  Both  (p*,e),  m (p*,e)+/c,  V  a  could  moving  costs,  as  each  point  (2).  counterpart  the  which  in  (u,e)  points in  1b.  1a, TC  for (1)  and  and  and so  (2)  are  K are  in  l i e  on  found  on  represented  m respectively these  two  by  points  Figures difference other in  1a  chooses e*.  in  between  1a  if In  stationary  In  is  i t  horizontal figure  and  authors.  figure  and  the  1b  the  regard,  consumption  wishes  this  to  remain  representation  because  V  *  >  V  s Weinberg, compensation V  IC  for  (p*,e*)  spend  is, on  IC  distances  between  be of  used moving  it  is  i t s  the  i l l u s t r a t e  costs  useful  bundle in  to  and  to  which  household  those  observe  the  current  the used that  by (3)  household  premises w i l l  given  indeed  p*  remain  *. m  Friedman, the = V  s  That  also  measure  this  vertical  1b.  may  our  and  and  Mayo  (1981)  define  household  (using  our  the  income  notation)  ( p * , e * - I C ) + /c  by (2.5)  m  is  the  maximum  transactions  costs  amount and  which  s t i l l  be  the as  household well  off  could moving  as  16  not.  It  8  is  distance IC  represented  between is  a  stationary, measure  of  suffer same a  points  (1)  of  loss  relative  to  a  for  those  resulting  benchmark.  household  figures  measure  loss  the  in  9  and  1a  1b  by  the  horizontal  (4).  for  those  world  households  without  households  transactions in  accordance  only  if  IC  >  moving  who  choose  TC.  with When  who  to  =p*  et  and  e  (j),  a  namely  move;  their  condition  that  V  *  > V  m There to  are  evaluate  example,  any  the  (1981),  EC  as  one  * .  number  of  the  could  equivalent 1  a  to  a l  the  (1981),  =e*  for  a l l  j to  our  condition  for  0  s of  other  relative costs  instead  al  is  is  and  relative  j tenures  TC  move  Weinberg p  remain  costs.  d i s u t i l i t i e s ,  Then,  moves  and  of  income  define  measures moving  and  compensation  an  analogous  which  could  staying. used  by  be  used  For  Weinberg  equivalent  et  compensation  follows:  V  (p*,e*+EC)  =  U*  (2.6)  s  This  is  the  household It  additional  for  measures  income  remaining  the  which  stationary,  distance  between  U*  would were and  just there  V  *,  compensate no  but  moving along  the costs.  the  s stayers'  Engel  curve,  (p*,e*),  X  rather  than  along  s The 1b.  solution  to  2.6  corresponds  (p*,e*).  X m  to  point  (5)  in  figures  1a  and  17  The T C  analogous  definition  for  transactions  costs  is  (p*,e*+EC-TC)  =  This  (2.7)  V*  s  m  measures  the  distance  between  U*  and  V  *,  along  X  m solution  1b.  And To  related for  by  :  V  The  given  a  as  to  corresponds  before,  summarize, to  the  move  are  Our  2.7  the we  to  household  have  move-stay  point w i l l  examined  decision.  (6)  move  three The  model:  s in if  EC  sets  of  *  > V  m  Income  Compensation: —  IC  >  Compensation:  EC  >  measures  These  conditions  e x p l i c i t l y possible  in  are  *  * > u*-v  terms  tenure  of  >  a  choices.  direct  but  the  u t i l i t y  * m  TC  * > u*-v s  equivalent;  conditions  TC  u*-v  -->  and  T C .  s  Equivalent  1a  s  u*-v  >  figures  corresponding  V  (p*,e*).  first  * m  is  comparison  expressed between  the  18  C.  Moving  The  Costs  and  presence  the  of  moving  consumers'  housing  demand  accommodation  for  Demand  demand  for  costs  Housing  leads  functions. x  for  1 1  a  to  discontinuities  Figure typical  depicts  2  household  in  the currently  a consuming  a  certain  quantity  x  .  In  this  section  the  s corresponding  price,  p  ,  applies  equally  to  movers  and  stayers.  the  demand  for  housing  a This to  allows  be  the  viewed  between  of  independently  of  discontinuities  from  2  the  costs the  on  effects  of  housing  occuring  p  and  at  moving  *  distinguish  neoclassical  discussions  with  moving  of  price  d i f f e r e n t i a l s  tenures.  Three figure  role  at  version  demand. p*  Two  (defined  may  households  adjust  their  accommodation  changes  the  The  third  these  inhibit  the  ease  levels  curve  in  employed  in  discontinuities,  forthwith),  which  economic  demand  typically  of  costs  in  the  are  with in  associated  which  response  to  environment.  discontinuity  occurs  at  p  (also  defined  below)  7  and  is  related  discrete  to  choice  residence  are  threshold  rather  Define the  S  household  tenure  regarding  such  as  switching.  that  than the  would  a set  the  we  must  smooth of  prefer  tenure model  of a  inherent a  vectors  remain  with  properties  household's  switching  transition  price to  The  between p=(p its  point  of  primary or  tenures.  ,p ,p ) o r s current  for  which  19  accommodation  bundle  (x  )  rather  than  bear  the  transactions  s costs  involved  demographic  S  in  moving,  given  characteristics  =  [p|  V  (p,e)  >  (d).  V  s  A  subset  of  S  i l l u s t r a t i o n  S  =  is  of  defined  [p|  That  expenditure  (e)  and  is,  (p,e)]  (2.8)  m  which is  household  p=(p  a  a  interest  for  ,p a  V  the  purposes  of  this  by  ,p a  )  and  (p s a  ,e)  >  V  (p ,e)] m a (2.9)  Then  p*  and  associated  p  are  *  with  defined  the  set  S  as  the  maximum  and  minimum  values  : a  p*  =  max  [p  | p  e S  a p  the  =  min  [p  | p  s u b - u t i l i t y  ] a  e  S  functions  ]  V  and m  p  and  for  a  typical  case  may  be  V  are  both  decreasing  in  s drawn  as  in  interval  [p  figure  3,  in  ,p*].  Over  which  a the  set  range  of  place  of  S  consists  prices,  of  the  the  residence.  closed  household 1  2  prefers  to  *  remain  in  its  this  present  21 Figure  Staying  Preferred  3  to  Moving  22  The  given the  existence  s u f f i c i e n t l y  following.  know  of  from  As  2.2  as  p  of  typical  case  costs  K and  accommodation  seems  V  (p s  considering  f a l l s  to  zero,  we  (2.10)  s  , e )  1  declines  3  until  p  =  a  e/x a  ( e / x , e ) = U ( x ,0) s  likely  that  s  rises,  V  V  a  (0,e) = U ( x ,e) = U (e)  a  Thus  in  transactions  the price  s  And  and p*  *  large  equation  V  p  s  ,  whereupon  s  = U (0)  s  (2.11)  s  is  somewhat  'pegged  as  shown  figure  i n '  at  i t s maximum  and  minimum  s values,  This  we  is  expect  in  that  in  contrast  V  ,  3.  to V  while  (p m a  ,e).  As  p  becomes  very  small  a  not unbounded,  obtains  very  substantial  m heights,  since  consumption.  the household Similarly,  as  can p  indulge  becomes  in  unlimited  large,  V  a f l e x i b i l i t y residual housing  in  funds  reducing for  commodities.  consumption  clothing  Thus  in  affords  more  m  housing  food,  housing  and other  general  so  as  to  have  essential  one expects  that  nonV  w i l l m  be  more  convex  from  the origin  than  is  V  .  Indeed  the latter  is  s quite off  conceivably  rather  quickly  concave as  i t  from nears  the origin i t s  since  endpoints.  i t  l i k e l y  drops  23  Finally  note  from  equation  2.1  that  V  decreases  with  K  m while  2.2  shows  that  V  is  invariant  to  changes  in  moving  costs.  s Thus  the  size  of  figure  composition the  set  costs  S  may  depend  involved,  c r i t i c a l l y  as  upon  i l l u s t r a t e d  the  in  4.  4  expect, the  the  transactions  Demand figure  of  curves  are the  corresponding  depicted measure  discontinuity  in  of  at  figures  the  x  set  tends  S to  to  different  5a  through  is  non-decreasing  become  values  5c.  of  As  K  one in  more  severe  that  households  in  would  K and  as  so  K  s increases. likely  This  to  This  says  relocate  nothing  when  the  more  costs  than of  S t a t e d a n o t h e r way, one 9 [p* - p ] / 3 K > 0 *  expects  is  givens  so  by (1)  reason  of  two  9 Vm/  3/c <  0  therefore  the  so  are  less  higher.  that (2.12)  for  V  doing  are  a l l  curves  prices  and  in  figure  V  in  4  do  not  m intersect, (2)  and  3 Vs/  3p  <  0 and  so  figure  4  is  s downward Thus  the  equality  transactions in  appendix  used  in  the  sloping. in  costs A,  with  2.12  holds  only  discontinuities. reference  empirical  chapters  to of  the  when  there  are  This  point  is  Linear  this  no i l l u s t r a t e d  Expenditure  dissertation.  System  24 Figure A Effect  of D i f f e r i n g V a l u e s of Kappa on  S  26  D.  Tenure  Choice  and  Transactions of  costs  discontinuity  the  absence  demand  for  The  =  in  nature with  {p|  V  demand  to  these  (p,e) o  >  V  Housing  for  above  home  constitute  ownership.  discontinuities  the  discrete  tenure  reference  for  discussed  costs,  due  of  Demand  as  the  moving  housing  understood  0  of  the  to  choice  the  (p,e)  nature  V  of  But  arise  (p,e)  r  >  V  even  tenure  distinct  source  in  discontinuities  following  and  may  one  in  the  choice. is  better  sets:  (p,e)}  o  s  and R  =  {p|  V  (p,e)  >  V  r The  (p,e)  and  V  o  decomposition  of  the  [p  ,p o  illustrated done  by  in  figure  King(l980)  illustrates  that  6  and the  (p,e)  >  V  (p,e)}  r  is  ]  plane  into  these  sets  as  r  implicit  Rosen(l979)  tenure  s  in and  switching  work  on  others. price  p  tenure  choice  Figure for  6  one  also  tenure  r depends  upon  Figure  the 6  decomposition ORS  =  {p|  prevailing  however shown V  (p,e)  is  in  a  >  V  =  {p|  V  in  specific  figure  o OSR  price  7  (p,e)  >  V  case  which >  V  r (p,e)  the  other. of  the  more  shows  six  d i s t i n c t  (p,e)} s  (p,e)  >  V  (p,e)}  general sets:  i  28  Figure 7  Owning v e r s u s R e n t i n g v e r s u s S t a y i n g  29  ROS  =  {p|  V  (p,e)  >  V  r RSO  =  {p|  V  (p,e)  >  V  r SOR  =  {p|  V  =  {p|  (p,e)  V  >  V  (p,e)  V  (p,e)  >  >  V  (p,e)} o  (p,e)  V  (p,e)} s  >  V  o  s Note  >  s  s SRO  (p,e) o  (p,e)} r  (p,e)  >  V  r  (p,e)} o  that  0 = ORS  V  OSR  R  =  ROS  V  RSO  S  =  SOR  V  SRO  and  where  V A  is  denotes study  valid  option  rent  Tenure household's while  of  only  to  the  the  housing  in  ORS  is  choice being  is  quantity  household's  housing  is  of  this  likelihood  model  demand ROS, only  of  for  decision framework.  discussed  in  which  transactions also  costs  neglects  the  ORS.  in  terms  with  any  of  of  the  Both  modelled  The  chapter  the  services  decision. are  sets.  ignores  one  accommodation tenure  two  which and  modelled  associated  upon  this  and  valid  conditional  maximum  intersection  six  sets  aspects  jointly  of  a  above,  demanded  econometric three.  probability  is of  within  the a  specification  for  30  NOTES  TO  CHAPTER  TWO  T h i s model i m p l i c i t l y assumes weak intertemporal separability, so e a c h p e r i o d ' s d e c i s i o n i s v i e w e d in i s o l a t i o n from t h a t of f u t u r e p e r i o d s . This characteristic i s s h a r e d by e a c h of t h e m o d e l s d i s c u s s e d in chapter one. One c o n s e q u e n c e of t h i s s i m p l i f y i n g assumption is that i t does not a l l o w the household t o d e c i d e in the current p e r i o d w h e t h e r i t w o u l d p r e f e r t o move i n t h i s p e r i o d o r the next. The s u p e r s c r i p t ' h ' has the f o l l o w i n g property": h h h V (p ,e ) = V (p ,e ) m m m m m m  "distributive  h  and  likewise  for  U(x  ,x m  )  and  other  multiple-argument  c  functions. D y n a r s k i (1986) makes a d i s t i n c t i o n between transactions costs (including intangibles) and r e s i d e n t i a l attachment, where the former e n t e r s the u t i l i t y f u n c t i o n as a negative, w h i l e the l a t t e r e n t e r s as a p o s i t i v e to household u t i l i t y . T h i s d i s t i n c t i o n i s o f no c o n s e q u e n c e here. The s p e c i f i c a t i o n chapters four and  o f /c(d) five.  is  spelled  out  in  more  The o p t i o n of r e n o v a t i n g is not allowed here, d e p r e c i a t i o n and maintanence expenditures are e x p l i c i t l y i n t h e p r i c e o f home ownership.  detail  in  although incorporated  F o r n o t a t i o n a l e a s e , we h a v e d r o p p e d e x p l i c i t r e f e r e n c e s the demographic variables (d) i n T C a n d K, a n d t o t h e superscript ' h ' wherever the context allows. The c o r r e s p o n d e n c e between p o i n t s in figures 1a a n d 1b i s not unique, except for the Engel curve X (p*,e) in m f i g u r e 1 a a n d i t s c o u n t e r p a r t V ( p * , e ) + /c i n 1 b . For m e x a m p l e , b o t h (3) and ( 3 ' ) i n f i g u r e 1a a r e m a p p e d into t h e same p o i n t i n f i g u r e 1b b e c a u s e t h e y a r e associated w i t h t h e same e x p e n d i t u r e a n d u t i l i t y levels.  to  31  8.  A c t u a l l y , Weinberg et a l (1981) s t a t e t h e i r income compensation i n two d i f f e r e n t ways. that state that i t is  definition On t h e o n e  (a) " t h e maximum amount of money t h a t t h e c o u l d s p e n d on t r a n s a c t i o n s c o s t s . . . w e l l o f f a f t e r t h e move a s before". On  the  other  hand  they  define  it  of hand  household a n d be as  as  (b) " t h e amount of money IC t h a t i f s u b t r a c t e d from a household's income would leave the household as w e l l o f f w i t h [x ] as i t w o u l d i f i t were t o consume s t h e o p t i m a l amount [x * ] a t a r e n t o f [p * x * ] . m m m These two use t h e i r the Engel  d e f i n i t i o n s are not e q u i v a l e n t . In the t e x t , I f i r s t d e f i n i t i o n because i t leaves point (4) on curve.  9.  O u r d e f i n i t i o n o f TC i s a r e l a t i v e l y b r o a d o n e i n t h a t i t i n c o r p o r a t e s p e c u n i a r y and p s y c h i c t r a n s a c t i o n s costs, w h e r e a s W e i n b e r g e_t a_l ( 1 9 8 1 ) i n c o r p o r a t e o n l y t h e former.  10.  To e  see =e*  that for  these  a l l  tenures,  IC —>  V  conditions  >  note  are from  equivalent 2.4  and  2.5  (p*,e*) > V (p*,e*-IC)+«(d) m P u t a n o t h e r w a y , t h e c o n d i t i o n IC > TC c o n d i t i o n t h a t (U*-V *) > (U*-V ), a n d s m V *. s The  terms  x  p  that  =p*  and  j  TC =V  m  11.  when  is so  (p*,e*). s equivalent to of course V * m  and p are "tenure neutral". This a a a p p l i e s e q u a l l y t h e r e f o r e t o owner o c c u p i e d and accomodation.  the >  exposition rental  32  12.  The arguments p r e s e n t e d i n t h i s s e c t i o n , and i l l u s t r a t e d i n f i g u r e s 3 t h r o u g h 5 a r e made w i t h r e f e r e n c e t o t h e subset S . S i m i l a r arguments apply to the r e s t of the set a S, b u t a t t e m p t i n g t o i l l u s t r a t e t h o s e a r g u m e n t s i n two d i m e n s i o n s w o u l d l i k e l y r e s u l t i n more c o n f u s i o n than insight.  13.  Here,  we  take  the  liberty  of  writing  "V(p  ,e)" a  for  "V(p,e)  where  p  =  (p a  ,p a  i  ,p a  )".  as  shorthand  33  III.  A.  Econometric  General This  Specification  Formulation  chapter  corresponding  to  chapter  The  two.  develops the  the  model  key  of  feature  each  household  has  from  among  into  ownership  accommodation  accommodation  (r),  or  the  must  decide  household  accommodation  services  terms  process. demand  arise  In  expected the  this  decisions  First,  and  the  stochastic  they the  under  the  choice  selected  in  the  household  Secondly,  further, h  (e  the  in  choice  which moving  rental  (s).  In  addition,  quantity  of  [1,H])  is  to  specify  applied tenure  in  the  choice  where  the  estimation and  housing  sequentially. a  is  tenure options  marginal  the to  decision  consume  i n i t i a l  on  denoted  the  on  That  its is,  actual  determines  conditional  (tenure) the  based  available.  household  consider  h v  joint  three  wishes  with  are  makes  i t  explain  is  into  actual  how  housing  To  presented  alternatives:  stationary the  modelled  tenure  tenure  moving  challenge  quantity  set  three  the  sets.  choice  model  this  (o),  opportunity of  of  upon  household  u t i l i t y  demand  consumed.  model, are  specification  housing  remaining  Econometrically, error  econometric  the upon  the  decision.  outcome  vector  associated  by  h =  (x  d o  ,x o  d r  ,x r  d s  ) s  (3.1)  34  where  d  (j=o,r,s)  is  either  0  or  1 depending  on  tenure  choice  j and  x  is  the  quantity  of  housing  services  demanded  in  tenure  j  j conditional out,  so  I  upon d  j  tenure  =  j  being  chosen.  Mixed  tenures  are  ruled  1.  J h  Denoting for  f(v  household  suppressed  h  on  )  we  the  as may  of  (where  hand  side  =  [P  *f  P  is  (.)]  for  observed h  *  [P  *f r  probability  (.)]  notational  vector  are  convenience)  d r  *  (P  r  of  outcome  subscripts  d o  o  the  an  the  d )  o where  density  write  right  h f(v  the  )  s  (3.2)  s  tenure  j  being  selected  and  f  j is  the  (.) j  density  demand  function  describing  the  distribution  of  x j  about  its  conditional  unit  the  been  residing,  demand  household  is  so  can when  uniquely Prob[x=x  |d  outcomes  in  tenure  definition, is  s  =1]  =  the  is  one  the  in  selected  only  which  dwelling  they  have  the  actual  level  random  sample  of  of  Thus,  1.  s  likelihood  household  stay  By  determined.  s The  mean.  of is  L  observing given  a  given  H  by  h  e  =  II  f (v  )  h  e  [ 1 ,H]  (3.3)  h h Substituting yields  the  maximand:  from  (3.2)  for  log-likelihood  f(v  )  function  and  taking  which  logs  serves  as  of  both  the  sides  object  35  L  =  L  [2 h  +  [L  j (d  h = Equation  d  *logP j  j  *logf o  Lt  3.4  +  is  and  is  the  general  found,  for  example,  *logf  (.)] r (3.4)  the  the  grouped  into  log-likelihood formulation in  second  observing  d r  been  Lt,  of  +  Ld.  has  The  (.) o  f i r s t ,  (1978).  ]  Judge  two  associated  for  quantal  e_t a l  component,  conditional  distinct  ( 1980)  Ld,  with  or  levels  the  isolation jointly  two from  the  numerous  ways  to  purpose  household  Sections which  B  then  (Ld)  C  to  and  the  this  of  x  chapter  tenure of  be  establish  in  mind  question.  decision  also  chapter  explores  model  the are and  of  are  specifications. is  to  allow  directly.  mechanisms  by  linked, conditional  function.  the  be  There  parameters (Lt)  to  in  same  estimated  specifications in  both  decision.  this  likelihood  bearing  model  tenure  econometric to  .  considered  the  competing  selection  the  often  allows  demand  3.4;  parameters  alternative  the  an  3.4  the  between  preference  preferences,  requirements  equation  are  Wise  r  framework;  underlie  developing  components  evaluates  household  of  unified  choice  household  respectively, demand  of  a  conditional  preference  and  these  the  demand  Equation  which  specify  in  housing  within  subsequent  arising  The  of  another.  preferences  underlie  the  one  determined  household  issues  aspects  and  log-likelihood  o These  choice  models  Hausman  x  the  tenure  response  represents  demand  terms;  Section  functional  form  D for  particular  Section  E  discusses  some  36  tradeoffs  between  modelling  tenure  discussion  of  assumptions tenure  error  B.  from  Linking The  tenure  of  the  =  is  given  2  2 h  In  order  choice  to  of  linking  the  d j  those  i t  for  function  specifications,  and  between  starter  G closes  case  section  conditional  values  the  for  with  function,  F  by  demand  the  chapter  likelihood  and  likelihood a  complete  based  on  to  Preference  the  previous  Parameters  function  section  related  to  as  *logP  (3.5) j  the is  parameters  necessary  parameters  to  the  to  (*)  underlying  formulate  probabilities  a  the  household  relationship  denoted  by  P  . j  particular, P  =  let  Prob[V  o P  =  Prob[V  r  V  =  >  Prob[V  s V  (*) j  chapter  two.  V  V  >  and  V  V  V  and  >  the  V  ] s  V  r  o are  > o  o  s the  and r  r  P  where  > o  a  sections.  log-likelihood  j  estimate  tenure  in  basis  likelihood  preceding  of  a  in  Probabilities  component  Lt  base  as  followed  Section  Tenure  choice  This  covariance  the  models is  terms,  process.  specification  probit  selection.  regarding  discussion  and  alternative  choice  iteration  logit  ]  (3.6)  s >  V  s indirect  ] r subutility  functions  from  In  37  that  The  expressions  the  V  may  be  in  are  3.6  expressed  developed  as  the  sum  further  of  two  by  assuming  distinct  j components: V  (*)  =  A  j where  A  (*)  +  (3.7)  X  j  J  (¥)  is  an  index  and  X  is  a  of  "expected"  or  "representative"  error  with  j u t i l i t y  random  term  E(X  )  j 3.6  may  P  then  =  be  Prob[(X  -X o  )<  -X o r  )<  Prob[(X  -X o s  )<  X  the  random  Prob[(X  r P  = s  Defining  as  (A  -A r  )  and  (X  o  -X s  )<(A -A )] o o s  -A o  )  and  (X  -X  r  )<(A r  -A s o  )  (A  (A  s and  variable  (X  -X r  X  ij be  the  for  random  probabilities  in  set  of  cumulative  differences.  Then  equations  may  3.8  the be  ,  let  j  joint  -A r  )]  (3.8)  s  )<(A -A )] s s r  -X i  [j=o,r,s] these  Equations  rewritten:  r =  0.  j  o P  =  G  (X j  ,X i j  distribution expression  further  for  ) kj functions the  simplified;  for  example  P  =  G  o P  =  G  r P  -A o  (A r  = s  (A o  G  -A r  (A s  ,A r ,A o  -A s  -A o -A r  ,A o  ) s  -A s  (3.9)  ) s ). r  38  The probit,  two  standard  arise  elements  X  from  in  models  of  alternative  equation  3.7.  quantal  response,  specifications In  logit  of  particular,  if  the X  j normally  and  stochastic  and  X  i  distributed,  so  too  is  X  ,  in  which  are j  event  the  probit  i j model  applies:  P  =  G  j where  (A j  $  -A j  is  , A i  the  -A j  )  =  $  k  (A j  standardized  -A j  , A i  joint  -A j  normal  )  (3.10)  k distribution  function  j corresponding The  to  other  stochastic  tenure  j .  assumption  components  X  t y p i c a l l y is  that  made  they  with  follow  regards a  to  Weibull,  the or  j extreme  value  distribution.  Because  the  difference,  X  , i j  between a  two  logistic  Weibull-distributed distribution,  G  in  random this  variables  event  i t s e l f  becomes  follows  the  j standardized model  =  G  (A  -A  j  j  With  either  in  directly are  joint  logistic  functon  and  so  the  logit  applies:  P  found  cumulative  found  the  j  the  -A j  3.10  f i r s t  linked in  ,A i  to  )  =  exp(A  k or  3.11,  component, the  )  /  j  household  subutility  i  the Lt,  index  exp(A  L  tenure of  the  selection likelihood  preference A  (•). j  )  (3.11)  i probablities function  parameters  *  are  which  39  C.  Linking The  Conditional  second  underlying  channel  household  conditional  demand  conditional  demands  assumed  to  density  functions  means  for  be  to  linking  by  for  on  is  tenures  o  within  underlying  centered  the  population,  Parameters  likelihood  mappings  households  from  entire  Preference  the  preference  functions  drawn  the  Demand  function  through and  each  r.  .  That  The  observed  group  are  probability  corresponding X  the  tenure  conditional  to  conditional  is,  (for  m=o,r)  m x  = m  where  the  function  X  (*)  e  (3.12) m  behavior  f  +  m  (.).  of  It  is  e  is  described  this  term  by  which  the  probability  appears  in  the  density  second  m component  of  Ld  the  =  log  [I  (d h  For  may  be  mean  derived  indirect  *logf o  empirical  conditional  likelihood  (.)  +  function;  d  o  *logf r  purposes  it  is  X  r necessary  (¥) e x p l i c i t l y . m immediately from the  u t i l i t y  index  A  (.)]  using  It  is  to  specify  assumed  corresponding  Roy's  here  the that  it  non-stochastic  Identity ; 1  m  X  (*) m  Doing  so  =  -OA  /ap ) m m  establishes  /  X  OA  (¥), m  /je) m  and  hence  (3.13)  c  , m  as  a  function  of  the  40  parameters  appearing  in  A  (¥). m  Thus  the  expression  for  the  density  function  f  (e  )  m appears  in  the  likelihood  conditional  function  w i l l  demand  serve  between  household  preference  (Ld)  observing  a  of  component,  to  forge  an  parameters  particular  outcome  Ld,  of  m the  additional  (*)  and  vector  the  of  which  link  likelihood  conditional  demands.  D.  Specifying There  to  choice  these  is  are of  derivable  levels  the  model.  is  of  Recall  Form  form  for  derived  chapter  two  each  of  which  the  household  which  tenure.  corresponds  necessitates  a  is  in  reflected  to  the  direct the  tenure;  The  comparison  each  direct  indices  index  these  occurrance  has  i t  and  of  subutility  of  the  vice of in  a  to  chooses  value,  be  comparison  assess  were  then  (or  alternative  household  enjoy  of  function  function  tenure  these  pertinent  foremost  u t i l i t y  of  each  of  The  u t i l i t y  household  highest  repeated  model.  indirect  would  Preferences  considerations  purposes  that  for  particular  this  from  index  that  or  direct  subutility welfare  Household  the  the  necessary  from  in  that  from  u t i l i t y  of  constraints  requirement  This  the  several  functional  the  e x p l i c i t l y versa).  Functional  the  level  choose  the  tenure  course  this  indexes,  expression  X  = i j  (A  -A i  )  in  the  j  choice  models.  preceding  discussion  (see  section  B)  on  as  tenure  41  The are  in  for  the  two  the  subutility  form  stay  of  form  level  housing  of  period  and  indirect  option  indirect  is  (j=s)  not  demand  therefore  due  housing  the  u t i l i t y  is  for  of  a  j=s  cannot  alternative  the  for  appropriate  maximizing to  indexes  direct for  constraint,  x  does  not  comparison  pose  theoretical units that  of  a  under =x  constructs;  both  indexes  functional  form.  Requiring  King  (1979) with  the  derive this  dual  the  not  comparisons  a are  Practical restriction parameters  on for  we  or  able the  dual  integral  considerations  both  to  so  the  do  form,  direct  prices  of  the  strongly namely, and  the  to  in  the  same in  or is  King  above,  u t i l i t y  several  functional  model  underlying  derive  out  It  For  indexes  indirect  function  f l e x i b l e  u t i l i t y  either  themselves.  discussed  form;  prior  comparable  or  rules  u t i l i t y  part  the  u t i l i t y  expressed  possible  translog  as  because  period  of  immediately  counterparts.  but  functional  are  direct  other  The  some  the  direct  given  functions  concern, an  a  in  current  and  always  indirect  most  the  not  for  be  the  demand  translog  is  notably  for  e x p l i c i t l y  was  i t  index  form.  option  as  perspective  therefore  form  that  forms,  (1980) for  are  However the  by  indirect the  and  the  s  from  e x p l i c i t l y  functional  the  stay  (j=o,r)  .  problem  measure  sense.  of  the  determined  a Exact  while  u t i l i t y  interpreted  prevailing  options  functions  was  be  moving  common  as  employed  by  Rosen  not  possible  forms and  to  Rosen  direct  developed  here.  favor  an  additional  that  i t  be  indirect  linear  specifications  in of  42  the  u t i l i t y  that  function.  having  an  f a c i l i t a t e s  index  its  v i r t u a l l y  employ  this  and  which  a l l  and  and  (1978)  (see,  McFadden  linear  for  McFadden  in  of  )  or  p.54)  argue  "greatly  interpretation",  logit  example,  (1973  (1975,  parameters  s t a t i s t i c a l  applications  assumption  Trost  is  estimation  indeed  Lee  Domencich  or  probit  Judge  et  Schmidt  and  models  al  (1980),  and  Strauss  (1975)). This  additional  functional  forms.  For  discussed  by  linear  parameters  is  in  shared  i t s e l f . by  Diewert  by As  Pollak  restriction  the  another  and  in  direct  of  CES  neither  One  the  functional  mentioned  above  is  by  the It  are  the  form  would  c r i t e r i a . described  Pollak  the  LES  direct  subutility  both  the  function  linear  in  does  appears However,  that  consider  model,  rather  (1986)  this than CES  share  characteristic by  the  forms  direct  and  the  is  dual discussed  indirect  same  translated  parameters. satisfy (C-D)  in  both  the  the  prerequisites  u t i l i t y  function.  its  direct  constant  Its  and  shares  implied  r e s t r i c t i v e .  appear  But by  are  but  more  specification  Wales  translated  Cobb-Douglas  form  and  form,  dual  the  which  manifestations.  C-D  the  u t i l i t y  form  linear-in-parameters indirect  of  several  quadratic  Diewert  self-dual;  specifications but  its  example,  are  the  (1975)  inverse  (1970)  forms,  example,  precludes  and  takes  on  no  the  functional Linear  Wales the  indexes.  form  satisfies  Expenditure  (1969,1978).  following  form  System  Applied for  the  to  a l l  our  (LES), our  indirect  and  43  h A  =  b(0) +  ln(e  m  -p m  7 -7 ) m a c  -  -  01np  /c(d)  (3.14a)  in for  m=o,r  h A  =  01n(x  s Here, b(0)  0, =  which,  ,  K{6)  )  -7 s  +  (l-0)ln(x  a  and  the  7s  are  01n0  + . (1-0) ln( 1 - 0 ) .  when  not  Cobb-Douglas assumption ( 1 971) )  2  The  equal  roots.  of  to  7s  homotheticity  The  LES  clearly  direct  But  examination  and  specification indexes.  through  satisfies  indirect of  the  as  the  is  not  linear  if  too  criterion d i f f i c u l t  the  model  our  well  origin  f i r s t  specifications  equations  However,  parameters  estimate  useful  be  estimated,  translation  distinguish  are  3.14 in  and  7  model for  and  parameters from  its  removing  (see  the  Pollak  is  be  mutually  indicates  are  held  that  for  namely,  that  derivable. this  the  u t i l i t y  constant,  the  linear  in  c satisfied.  where while  criterion,  parameters  7  a  be  are  7s  to  .  the  to  (3.14b)  c  parameters  zero,  The  )  -7 c  the  7s  holding  If  estimation  are  estimated  the  the  7s  should  freely,  fixed  at  prove  one  can  various  values. Thus  the  LES  compromise  between  parameters  form.  this  applied  specification variable It  is  research.  appears  expenditure  therefore  to  offer  shares  selected  for  a  reasonable  and  a  linear  in  the  purposes  of  44  E.  L o g i t In  vs  c h o o s i n g  f a c t o r s  must  p o s s i b l e c h o i c e  be  i n  parameter The  f a c t o r s ;  s e c t i o n  F  the  i s  3.10  of  i s  the  p r o b i t  c o m p u t a t i o n a l  the  random and the  t h i s  d i s c u s s e d  models  (3)  the  maximum  w i t h i n  in  the  l i k e l i h o o d  i s  on  of  good  i t e r a t i o n  the  f i r s t  r e s e r v e d of  (2)  tenure  f o r m u l a t i o n  focuses  e s t i m a t e s  s e v e r a l  t r a c t a b i 1 i t y ,  v a r i a b l e s  s e c t i o n  s t a r t e r  for  the  c o n t e x t  the  the  a d v a n t a g e s  in  v e r s u s  p r o b i t  s p e c i f i c a t i o n . d i s p u t e  r e g a r d i n g  p r a c t i c a l i t y  a d v a n t a g e s w i t h  and  (1)  for  in  of  l i t t l e  These  method  r o l e  l o g i t  3.7,  e s t i m a t e s  i t  c o m p u t a t i o n a l  e q u a t i o n  e q u a t i o n  f u n c t i o n  There  model.  between  d i s c u s s i o n  where  l i k e l i h o o d  the  c o n s i d e r e d :  d e c i s i o n  p r o c e s s .  of  between  c o v a r i a n c e  i n i t i a l  two  P r o b i t  can  3.11.  of be  the  r e a d i l y  E x p l i c i t  p r o b a b i l i t i e s  P  l o g i t  noted  by  c a l c u l a t i o n  which  l i e  at  the  c o n t r a s t i n g  by  the  terms  the  p r o b i t  h e a r t  of  the  j l i k e l i h o o d the  f u n c t i o n  d o u b l e  =  0  j <t> (  r e p e a t e d  n u m e r i c a l  e v a l u a t i o n  of  i n t e g r a l  *  where  r e q u i r e s  ,  (  i  '  k  )  d  i  d  (3.15)  k  j )  is  the  j o i n t  normal  d e n s i t y  f u n c t i o n  and  the  j l i m i t s  of  i n t e g r a t i o n  a r e  from  minus  i n f i n i t y  to  A  and j i  r e s p e c t i v e l y . of the  the  These  a l g o r i t h m  l i k e l i h o o d  s  c a l c u l a t i o n s  which  seeks  f u n c t i o n .  the  are  r e q u i r e d  s o l u t i o n  at  each  p a r a m e t e r s  A jk  i t e r a t i o n m a x i m i z i n g  45  In  contrast,  the  logit  model  in  equation  3.11  expresses  P j  in  closed  form;  consequent Albright  et  al  of  integration  computation who  report  iteration  time that  exceeded  is  are the  the  required. evident  probit  logit  The  in  a  study  by  CPU  requirements  by  a  ease  by  15.  logit  obtained  in  (1977)  per  However, the  numerical  savings  requirements factor  no  the  form, at  covariance  the  advantages  of  computational  particularly  in  its  expense  matrix  for  of  the  simplest  restrictions random  terms  manifestation,  imposed X  enjoyed  in  upon  are  the  equation  3.7.  Thus  j for  example,  i t  log(P  follows  This  indicates  logit  model  alternat  k  to  be  that not  of  assumption  odds  moving,  so  of of  one  that  would  error the  being  make  together"  the  when  as  households  event  the  choosing the  tenure  presence  of  j  over  k  in  the  other  ives.  perceived  "lumped  that  (3.16)  independent  Independence dubious  3.11  jk  that  are  equation  ) = A  /P j  from  as  a  terms  similar.  primary o  For  in  and  positive  r  would  3.7  one  between be  requiring  is  question  example,  distinction  alternatives a  equation  alternatives  tenures  expect  in  a  are could  argue  moving  perceived  between  and  as  relocation.  correlation  l i k e l y  being In  X  this  and r  a  willingness  indicates  some  or  aversion  willingness  to or  relocate aversion  to to  rental  X  ; o  accommodation  relocate  to  self-owned  46  Figure 8  S t r u c t u r e of Tenure D e c i s i o n  7  47  accommodation. Were be  this  better  three  and  applies. best  so  modelled  example  the  tenures  o  between McFadden demand,  the  in  and  Vs  r  a and  that  estimation  in  figure are  figure  terms  of may  a  argue,  than  by  8a.  perceived  to  be  sensible  logit  model"  household  first  make  upon  binary  in  decision  sequential  max[Vr,Vo].  biases  8b  8b,  conditioned  sequential  and  household  "independent  move/stay  (1973)  practical  by  household  by  the  alternatives  Whereas  followed  case,  represented  tenure  another  the  a  a  the  modelling means  resulting  of from  of  In  figure  8a  the  independent  of  one  (Amemiya  (1981))  making  choice  structure.  binary  decision  decision  to  where  and  context  would  decision  decision  Domencich  structure  of  move. the  McFadden  the  similarly  between This  is  (1975)  decision  mitigating  For  comparison  modelling  the  is  urban  is  and travel  process  is  a  potential  perceived  alternatives. Another the is  error termed  method  of  allowing  structure  in  3.7  the  generalized continue  nonindependent  extreme  with  is  the  value  move/stay  for  also logit  (GEV)  more due by  model  example,  flexible  to  McFadden  Amemiya by we  of  (1981),  and  (1981),  Maddala may  treatment  or  the  (1983).  To  assume  that  X  and r  X  jointly  follow  adheres  to  a  bivariate  extreme  value  distribution  while  o X  a  univariate  extreme  value  s have  the  probability  of  staying  given  as  distribution.  Then  we  48  P  = expA s  / (expA s  + M)  (3.17)  s  where 1 -a M = [ e x p ( A /1-ff) + [ e x p ( A / 1 - a ) ] o r  (3.18)  i s a " w e i g h t e d a v e r a g e " o f e x p ( A ) a n d e x p ( A ), and a i s a o r coefficient  varying  between  0 and 1 a s X o  uncorrelated  or p e r f e c t l y c o r r e l a t e d ,  and X a r e e n t i r e l y r  respectively.  Then  1/d-o) P  = (1-P ) [ ( e x p A )/M] o s o  (3.19)  and P  = (1-P ) ( 1 - P ) s o  r This  nonindependent l o g i t  between  of  i s made a c c o r d i n g  move/stay d e c i s i o n  sets  (those  logit  a dichotomous l o g i t model  McFadden  f r o m 3.11  logit  where,  requiring  a certain  framework.  kind  while  the stay Note t h a t  alternative the independent  i s a s p e c i a l case, corresponding  t o a=0.  of a l t e r n a t i v e  f o r t h e w e i g h t i n g p a r a m e t e r a.  sequential model.  using  model  of w e i g h t e d a v e r a g e  (1981) p r o v i d e s a d e t a i l e d c o n s i d e r a t i o n  specifications The  the c h o i c e  t o a dichotomous l o g i t  the r e l o c a t i o n a l t e r n a t i v e s against  within  the  i s a t t r a c t i v e i n that  t h e two s i m i l a r a l t e r n a t i v e s  relocation) the  (3.20)  decision  Amemiya  framework  need n o t be c o n f i n e d  (1981) d i s c u s s e s  our t e r m i n o l o g y :  a sequential  to  probit  49  P  = <t> ( A ) s s  s P  =  ( 1 - P ) $ (A ) s o o  =  (1-P ) (1-P )  o p r This burden not  s  clear  binary  attest, models  extreme  full  force  t o ease  probit  logit,  model.  only  since  structure.  they  each  probit  i s  over the  rely  and  s i m i l a r due t o s i m i l a r i t y  decisions  i t  on an  A n d a s Hausman a n d W i s e  of the binary  the advantages  where  However  has any advantages  o f t h e d i s t r i b u t i o n s upon that  the computational  which  a r e based  (except  they  of the p r o b i t  binary  a r e based.  model  o n n-way  i n the  come  into  comparisons  n>2. The  logit  is  helps  probit  the properties  tails)  suggests  and  decision  are rather  This  for  the sequential  or nonindependent  essentially  logit  structure  by t h e u n r e s t r i c t e d  that  sequential  (1978)  r  sequencing  posed  (3.21)  third  factor  alternatives,  possible  important function  in addition  covariance  the formulation  estimates.  to consider  Lee and Trost  weighing  the probit  to computational  between  of good  when  the tenure  initial (1978)  maximum  argue  that  when  searching  f o r the global  which  i s highly  nonlinear  and  tractability  choice  error  terms,  l i k e l i h o o d parameter this  maximum  i s particularly of a l i k e l i h o o d  i n parameters,  as i n our  case. Although for  the a v a i l a b i l i t y  the l i k e l i h o o d iteration  decision  between  the probit  o f good  procedure and l o g i t  s t a r t e r value may  have  models,  estimates  a bearing  on t h e  the discussion  of  50  starter  values  likelihood that  F.  we  is  function  now  in  the  specification.  Function  likelihood  proposed  placed  context It  is  of  to  the  maximum  this  discussion  turn.  Likelihood The  best  by  King  Specification  function  set  out  in  section  A  is  of  a  gendre  (1980): d  L  =  n h  While  [P  II j  well  j  and  another. into  )]  j  j  also  to  handling  implicitly  continuous  This  separate  is  multiple  restricts  decisions  shown  and  (3.22)  j  disposed  specification discrete  (e  f  by  distinct  to  be  tenures, the  of  tenure  and  )  error  terms  uncorrelated  delineation (P  this  the  for  with  decision  the  one  structure  conditional  demand  j (f  )  components.  Put  another  way,  3.22  implicitly  constrains  j cov(X  ,e ij  from may  )  zero, lead To  =  0  for  a l l  ( i , j ) .  If  in  fact  cov(X  j  to  ,e i j  then  the  sample  explain  implicit  assumption  s e l e c t i v i t y  further,  bias  consider  in  three  to the  the  contrary  parameter  sets  )  H  differs  j in  3.22  estimates.  [j=o,r,s]  where  j h a  household  h  belongs  to  H  if  and  only  if  j the  knowledge  our  expectation  tenure  j .  that  From  of  household the  3.12:  d  =1.  In  general,  j h  quantity  has of  chosen housing  tenure he  j  would  may  influence  select  in  51  h E(x  h | heH  j  )  =  X  j  (*)  +  E(e  j  j h  =  X  | heH  (¥)  +  j  h  E(e  | X  j  )  j  h <A  i j  and  X  j i  <A kj  ) jk  h ¥• X  (*)  =  E(x  )  j since,  in  (3.23)  j  general,  cov(X  ,e  )  ij A  more  f u l l y  covariances  more  general  *  0.  j model  e x p l i c i t l y .  would  This  is  seek  to  incorporate  done  by  allowing  the  these X i j  and  e  to  be  j o i n t l y  distributed  by  a  common  density  function,  j as  shown  here  d (e  •  [\ _  \ g (e ,X ,X ) „ r r sr or  before, A  cases. a l l  and  L e  dX  dX sr  dX  ]  o  ro  ]  r  or  dX  is  to  be  maximized  ]  s  L  in  3.24  (3.24)  subject  to  the  parameters  3  for  reducing  allows  one  -A,r [ $ g (e ,X ) _ o o ro  h  so  )  example,  =n  ro  dX  ,X  .  expression For  so  dX  j  households  L  o  (X  j i The  )  °K _b o.  as  defining  ,X  h  g  where,  ,X  to  this  has  some  to  rewrite  a L  interesting  two in  tenure  simpler  special  problem  for  form:  d dX  ]  o  ro  0 0  d [^ K  g  (e r  ,X r  ) ro  dX  ] ro  r  (3.25)  52  This owning  likelihood  and  stayers.  renting; When  g  function no  and  distinction g  o 3.25  corresponds  Their  model  is  stage  procedure  which  may  in  iteration  are  joint  model  set  is  only  made  normal  two  tenures,  between density  movers  and  functions,  r to  the  developed for  turn  point  parameters  *  for  the  producing  serve  as  out  that  out  by  Lee  purposes  consistent  starter  attempts  for  the  demand  =  (*)  +  h x  and  of  Trost  presenting  parameter  values  (1978).  for  the  a  two  estimates likelihood  use  functions  OLS  from  to  estimate  the  3.12  e  j  the  to  h X  j on  for  routine.  They  based  allows  (3.12) j  sample  set  H  may  result  in  biased  and  inconsistent  j h estimates  since,  in  general,  E(e  |heH j  the  assumptions  likelihood a  danger  function  that  sufficiently effective The methods  underlying  these close  highly  OLS to  starter  OLS  in  procedure.  nonlinear  true  0,  violation  of  j  estimates  the  #  w i l l  in not  parameter  When  the  parameters, prove  values  to to  there  is  be serve  as  values.  remedial outlined  is  the  )  procedure by  Heckman  which  they  (1976),  propose,  involves  similar  obtaining  to direct  h estimates  of  E(e  |heH j  non-zero H  . j  Then  mean OLS  for  )  and  using  these  estimates  to  adjust  the  j the  error  estimates  for  term the  in  3.12  adjusted  for  the  demand  selected functions  sample  53  h  h (x  are  |heH  j  j  ) = X  j  + E(e  (*)  j  shown  by  Lee  and T r o s t  estimates  of  *.  For  have  E(TJ )  |heH  the  and  by  j  ) +  n  (3.26) 3  Heckman  new e r r o r  to  terms  yield  consistent  introduced  in  3.26  we  0.  =  j If are  one  further  versus  were  inclined  arguments  the  logit  to  to  adopt  be made  model.  The  this  in  two stage  favor  reason  is  of  that  method  the the  probit  there model  expression  for  h E(e  )  |heH  has  been  shown  by  these  authors  to  be  J  j  relatively  forthcoming  when  g  in  normal.  )  , X  (e j  previous  j  3.25  are  the  joint For  in  that  functions event  i j h  E(e  h )  |heH j  = cov(e  j =  cov(e  by  )  , X j  since  density  , X ) j i j  E ( X i j  [-<}> ( A  )"/*  J  i j  definition  Ji  (assuming  h |X i j  (A  J  the  < A  )  Ji  )]  (3.27)  Ji are  X  normally  distributed),  i j h  E(X  h  ij  i j =  Heckman,  (A  )/# j i  (A  (A j  expression  1979).  j )  ( z ) / * (A j  ) dz  j i  dz  3 Ji  3  j  z<t>  - ~  <S> ' (z)/4>  -\  «  latter  ) = ^ j i  J>  This  - " r ^  < A  | X  )  (3.28)  j i is  the  inverse  of  M i l l ' s  ratio  (see  54  The probit  Lee  and  Trost  (1978)  procedure  then  entails  use  of  the  model P  =  $  j  (A  )  (3.29)  j i  J  h to  retrieve  consistent  estimates  of  A  ,  and  thus  of  E(X  ji <  A  ).  When  these  latter  estimates  h |X  i j  are  added  as  i j  independent  j i variables  to  two  results  are  now  of  the  equation ensue.  free  of  error  3.12  for  the  purposes  F i r s t ,  the  OLS  estimates  sample  terms  for  s e l e c t i v i t y the  bias  subsample  of of  since  H  OLS  have  regression,  the  the  parameters  nonzero  been  means  adjusted  for.  j Second,  by  virtue  of  equation  3.26, h  recently  added  regressor  E(X  estimator  of  cov(e  (1978)  may for  modify the  ,X  terms  e  for  For the  normal  example,  tenure  if  choice  for  the  conditional  distributed,  the  joint  estimate  for  the  A  )  w i l l  itself  be  a  j i ).  i j  procedure  bivariate  distributions. framework  the  < i j  j We  OLS  h |X  ij consistent  the  advocated case one  to  Lee  and  accommodate  wished  model  demand  by  to  while  other  retain  allowing  functions  to  Trost  be  a  logit  the  error  normally  j density  function  g  (e j  would  have In  to  this  be  a  case,  normal-logistic the  expression  density analogous  ,X j  )  from  i j  function. to  3.28  is  3.25  *  55  h E(e  h |heH  j  )  =  cov(e  ,X  j  j  )  E(X  i j  |X i j  <  A  i j  ) j i  h =  cov(e  ,X j  )  I(A  )  i j  (3.30)  j i  where  I(A  )  =  [1-F(A  j i  )]A  -  j i  j i  1 +  exp(-A  F(A  )*ln[F(A j i  )]  (3.31)  j i  and F(A  )  =  j i  Appendix  B  contains  3.31.  When  choice  decision  ratio  a  found Thus,  model  this  detailed logit  (3.32)  and  method  for  the  error  terms  is  of  the  applied  replaces  the  expression  to  the  inverse  in  tenure of  M i l l ' s  3.28. obtaining  tenure  decision  are  e  derivation  model  expression  3.27  governs  demand  a  binomial  in a  ) j i  starter and  normally  values  when  the  distributed  when  a  logit  conditional is  as  follows.  A  .  Second,  j First,  use  a  logit  model  to  estimate  the  index  j i substitute  these  values  I(A  for  estimates )  thus  into  obtained  3.31 as  and  use  the  additional  estimated  regressors  for  the  j i conditional nonzero  demand  mean  of  e  function for  the  in  3.12.  sample  set  j that  proposed  by  Lee  Doing  so  H  a  in  adjusts manner  for  the  similar  to  j and  Trost  (1978)  but  allowing  for  X  to i j  be  56  l o g i s t i c a l l y To has  a  recapitulate  potential  covariance decision  of  biased  and  starter  in  in  for  sample  enjoy  section  E  e  and  X  j which to  have  and  not  allow  discrete  terms the  are  demand  therefore  proposed  a  stage but  functions  in  tenure  the  decision. above  while  deriving  search  the not  The  removes  advantages  of  as  procedure their  method  likelihood allow  for  a  logit  modification  this  the  to  restriction  logit  model  satisfactory  algorith  be  attractive  two  does  w i l l  procedure.  density  so  fact  less  bias,  and  3.22  continuous  functions  be  iteration  in  for  and in  selection  likelihood  function  the  for  w i l l  proposed  despite  and  as  starter the  presence  bias.  Notwithstanding  of  error  does  function  sample  the  selection  likelihood  these  binormal,  method  the  for  and  this  are  it  likelihood  joint  to  that  likelihood  terms  (1978)  govern  one  in  the  estimates  the  for  3.25  Lee-Trost  discussed  of  for  the  to  allows  If  OLS  Trost  that  framework  values  error  inconsistent  and  function  so  then  corrects  assumes  drawback  the  values  Lee which  b r i e f l y ,  functions.  correlated,  the  distributed.  the in  the  above,  3.22  the  which  likelihood  distinction  does  not  between  allow  functions  in  for  3.24  the  covariance  and  3.25  i j do  date  housing  may does  is  more  not  demand  themselves evidence  be  apparent  suggest  functions.  conclude weak".  that Rosen  a  than  strong For  real. degree  example  "simultaneity (1979)  The of  Lee  evidence  simultaneity and  does  applies  empirical  the  Trost  occur, same  bias  (1978)  albeit method  the and  in  57  finds the  that  the  housing  demand  significantly 'missing  resulting and  from  estimate  probit  zero.  variable'  has  of  the  covariance  equations  According  does  to  essentially  no  not  Rosen,  of  errors  differ  "omission  impact  on  in  the  of  the  estimated  coefficients. This the  more  fully  required course  evidence  from  of  general the  action  estimation  suggests  that  likelihood  practical which  purposes  the  cov(e  ,X  may  L  rewrite  likelihood  3.24  may  is  to  =  0.  function  in  be  Therefore,  assume  Using  not  of  a  for  this  assumption  i j 3.24  as  follows:  d  n  =  the  )  in  advantages  perspective.  i t s e l f  j we  function  empirical  suggests  that  theoretical  [f h  (e o  )  g  o  (X  ,X  )  o  so  ro  (X  ,X  )  dX  dX so  ]  o  ro d  [f  (e r  )  g  r  r  sr  ,X  )  dX  dX  or  sr  ]  r  or d  [  g  (X s  os  dX  rs  dX os  n  [f o  h  This  is  (e o  )  section  A  in  section  this  function decision.  to  ]  [f  other  which  in  U r  the  )  that  of  d r  P  s  (3.33)  s  likelihood in  equation  this  using  course  ]  r  the  reappears  with,  P  r  than  suggests  proceed If  d o  o  nothing and  P  s  rs  d =  ]  is  logit the  the to  function 3.22.  discussed  The  discussion  appropriate model  estimation  the i t  in  likelihood  tenure  appears  that  58  troubles bias,  then  section  G.  are  arising  the  may  modified  be  called  Specification The  f u l l  which  of  model  log-likelihood  may  be  Lee-Trost  rooted  in  procedure  sample  outlined  L  =  =  this  Base may  Model  now  be  specified,  beginning  with  the  function;  [L  Lt  in  upon.  h log  selection  I  d  h  j  +  Ld.  *logP  j  h ]  +  [I  j  I m  h  d m  *logf  (e )] m m (3.34)  h=(1,H) j=o,r,s m=o, r  This the  likelihood pattern  which  function  describes  of  tenure  choices  actually  appear  in  our  and  the  probability  conditional  of  observing  housing  demands  sample. h  The  tenure  choice  probability  for  household  h  (P  )  depends  j upon  the  expected  u t i l i t y  for  tenure  j  (A  ),  as  given  by  a  j generalized  extreme  value  h P  (nonindependent  logit)  model;  a =  exp[A  m  / ( 1 - O ) ] * M  /D  (3.35a)  m h  P  = s  exp[A  ]/D s  (3.35b)  59  where h M  =  exp[A  /(1-a)]  +  exp[A  o  /(1-a)]  (3.35c)  r  h  1-a  D  =  exp[A  ]  +  M  (3.35d)  s The  expected  u t i l i t y  is  described  by  an  LES  model,  so  that  h A  =  b(/3)  +  ln(e  m  -p m  |31np  y -y ) m a c  -  (3.36a)  K  m for  m=o,r  h A  =  ]31n(x  s The  ) +  -y s  (l-/3)ln(x c  generalized  logit  )  -y  a model  (3.36b)  c embodied  in  Lt  is  complemented h  in  3.34  by  Ld,  which  incorporates  density  functions  (f  )  for  m the  households'  conditional  share  equations  (s  =p m  h f  = m  (27.0m  2-1/2 )  2 exp[-e  x ); mm  so  that  2 /2a m m  ]  (3.37a)  where h (e  )  =  E(s  m =  [p  )  m  to  six  likelihood  basic  m  (1-/3)7 m  The  s  + a  0(e  -7 m  function  parameters;  )]/e  -  s  c in  j3,u,7  3.34  is  maximized  ,K ,and  ,y a  (3.37b) m  5  c  o.  The  with  respect  results  of  60  this  estimation  following  a  procedure  discussion  of  are data  detailed and  in  chapter  variables  in  five,  chapter  four.  61  NOTES  1.  TO  CHAPTER  THREE  R o y ' s i d e n t i t y c a n n o t be i m p o s e d upon t h e stochastic component of household u t i l i t y in this context without i n t r o d u c i n g an u n w a n t e d i n t e r d e p e n d e n c e b e t w e e n e and m translation  parameters  X  . m  2.  The  ) i n t h e LES specification i are sometimes r e f e r e d to in the Stone-Geary sense as "committed bundles". However, that interpretation is not a p p l i c a b l e h e r e , w h e r e we h a v e n o p r i o r expectations r e g a r d i n g the s i g n of 7 . i  3.  F o r t h e g e n e r a l l i k e l i h o o d f u n c t i o n s p e c i f i e d i n 3.24 i t is assumed t h a t the housing d e c i s i o n i s s e q u e n t i a l . That is, households f i r s t s e l e c t t h e i r t e n u r e m a r g i n a l on t h e a c t u a l opportunity sets. Secondly, the household determines the q u a n t i t y of h o u s i n g i t wishes t o consume c o n d i t i o n a l upon that tenure.  4.  In c o n t r a s t , G i l l i n g h a m and Hagemann (1983) do find s i g n i f i c a n t e v i d e n c e of s i m u l t a n e i t y b i a s . They a t t r i b u t e their different findings to differences in the data set u s e d by b o t h R o s e n ( 1 9 7 9 ) and L e e and T r o s t (1978), as well as t o d i f f e r e n c e s i n the s p e c i f i c a t i o n of housing expenditures for owner-occupiers.  5.  As d i s c u s s e d demographic  in chapter variables.  (7  five,  /c(d)  is  i t s e l f  a  function  of  62  IV.  Data  and  A.  Introduction This  arising  chapter  from  That  model  data  set (1)  Variables  the  addresses econometric  assumes  are  some  that  available x  of  model  the  outlined  observations for  —This  each  of  variable  practical  for the  is  a  in  each  data  issues  chapter  three.  household  following measure  of  in  variables: the  flow  s of  accommodation  dwelling during  the  housing  (2)  d  x o  unit  services  in  which  period  decision  — I f  a  the  prior is  from  household  to  being  household  derived  that  in  the  resided  which  the  modelled.  moves  to  a  owner  o  occupied period  dwelling  (ie,  if  d  unit  during  =1),  then  flow  of  the  current  observations  are  o required  for  services,  x  the ,  derived  accommodation  therefrom,  o  (3)  d  x r  — A  similar  requirement  applies  r  household  chooses  accommodation.  to  move  to  rental  when  the  some  63  (4)  x  —Observations  are  required  for  the  c  (5)  consumption  of  p  the  —This  is  goods  unrelated  user  cost  of  which  own  the  to  housing.  housing  capital  o for in  households which  flow  (6)  p  they  price  --This  reside.  rather  is  the  Note  than  flow  dwelling  a  that  stock  price  unit  this  is  a  price.  of  accommodation  r for This  households measure  who of  reside  gross  in  rent  rental  units.  includes  u t i l i t i e s .  (7)  p  —Current  period  price  of  the  household's  s accommodation,  x  ,  from  the  previous  period.  s This  may  differ  from  p  or o  (8)  p  —Current  period  p  . r  price  of  other  c consumables,  (9)  e  —Income  normalized  after  taxes  at  for  1.  the  household,  o were  it  occupied  to  choose  to  relocate  accommodation.  Based  to on  owner average  income  (10)  e  for  1977,  1979,  and  --Income  after  taxes  for  1981.  the  household,  r were  i t  to  choose  accommodation. 1977,  (11)  e  1979,  —Income  to  relocate  Based  and  on  to  rental  average  income  for  1981.  after  taxes  for  the  household,  as  s defined  above  for  y  or o  choose  to  unit.  Based  1979,  Many  of  construction.  these  and  remain on  in  y  ,  were  i t  to  r i t s  average  present income  dwelling for  1977,  1981.  variables  require  careful  d e f i n i t i o n  and  65  B.  The  Data  This Soc i a l on  a  research  Change  nationwide  designed, quality  as  of  pertinent  The 1981; This  into  they  move  sets  which  information  provide so  set.  The  (QOL)  is  survey  i t  touches may  be  based  is  information  which  three  c r i t e r i o n  1979  1977  period',  We  move  be  waves;  for  in  our  require  to  and  on  upon  the  many  readily  e l i g i b l e ,  survey  to  be  a l l  dwelling  excludes  w i l l  serve  here.  This  drawn  and waves.  examination  example  p a r t i c u l a r y as  1979  three  for  year  undertaken  1977,  of  information  the  requirement  survey  e m p i r i c a l work  'previous  QOL  interviewed  essential  The  the  in  decisions.  otherwise  from  Survey  The  data  are  households  Canada.  Life  doing  conducted  This  might  to  housing  important  units  of  data  model.  move-stay  the  In  households  from.  of  for  suggests,  our  an  r e l a t i v e l y new  households.  Canada.  are  many  dwelling  the  in  surveys  households'  to  name  a  Quality  of  f i n a n c i a l and  satisfies  year  sample  l i f e  where  Census  Canada:  the  incorporated  the  in  employs  upon  regards  on  units  many the  as  both  data 1981  the  base  allows in  x  reference  ,  the  s quantity Using  1979  surveys price  of  to  housing as  the  play  a  services  base  year  role  in  consumed also  in  allows  defining  the the  previous 1981  permanent  period.  and  income  1977 or  housing  trends. Other  selected. excellent  data The  sets CMHC  detail  on  were  also  Survey  of  dwelling  considered  before  Housing  Units  structure  and  (SHU)  the  QOL  set  was  provides  financing  attributes,  66  but  suffers  and  intra-CMA  losing  its  changes  and  lack  taken  Michigan  housing  geographically d i f f i c u l t i e s  would  place Panel  would  be  taxes  the  too  much  to  chapter.  variables  provided  transformations of  to  poor.  expect  one  data the  this  that Also,  to  1974  is  States  because  is  was  on  sample so  many  years.  (PSID)  survey the  rapidly  survey  Dynamics  United  precisely  the  of  data  markets  and  Income  the  SHU  attributes  income, is  that  provide  data  on  local  find  data  set  grants.  Instead, by  the  1971  trying  or  this  sections  over in  the of  neighborhood  housing  focus  is  and  A  remaining  today's  Survey  arise  corresponding  These  to  However  variables of  addition,  since  dispersed  on  In  information  housing-related It  information  location.  considered. the  of  a p p l i c a b i l i t y  have  The also  from  to must  set  QOL  to  indicated  convert  into  data  chapter.  those  a  the  set of  with  in  section  of  a  new  set  variables.  set  are  described  in  the  67  C.  Measuring  1.  Hedonic Two  Accomodation index  issues  accommodation there the  is  a  quantity issues the  one  ownership  services  is  (1970)  or  x  the  of  of  the  find  for  a  in  a  viable  consumed  appropriate  which  the  discussed  use  actually  meaningful  must  indexes  The  ,  a  quantity  developing  equations  into  are  in  services  question  attributes  housing  arise  regression  Secondly,  of  seek  index  suitable  turn,  housing  and  where  of  of  and  discussion  F i r s t ,  form  for  observed  quantity.  reconciling  rental  the  household.  translate  means  ownership  a  dimension  to of  by  measure  sectors.  the These  focuses  f i r s t  on  sector. of  hedonic  quite  Rosen  indexes  common  (1974)).  quantity  of  (see, Its  owner  to  measure  for  example,  purpose  is  occupied  to  the  flow  Kain  of  and  develop  accommodation  housing Quigley  estimates, services  o consumed  based  on  a  (nx1)  vector,  z  ,  of  attributes  for  owner  o occupied  dwelling  units.  In  particular,  we  have  the  linear  relationship: m(x  )  = CJ ' z o o  o  ,  or  (4.1a)  -1 x  =  m  (CJ ' z ) o o  o where  is  CJ ' o  some  is  a  (1xn)  monotonic  vector  (4.1b)  of  coefficients  transformation  of  x  . o  or  weights  and  m(  )  68  as  a  Equations  4.1  monotonic  transformation  observed what  housing  vector  ought  to  of  be  describe  the of  attributes.  and  some  The  characteristics  included,  consumption  (2)  of  housing  services  weighted  average  of  relevant  (or  questions  are:  transformations  which  set  of  (1)  thereof)  weights  is  appropriate? It to  is  satisfy  reasonable two  1.  to  expect  an  index  of  housing  consumption  c r i t e r i a : Any  two  dwelling  vectors also  of  have  index.  units  observed  rules  identical  characteristics  identical  This  with  values out  of  the  the  use  should measured  of  v  ,  the  o owner's sell 2.  The  evaluation  for,  as  weights  market's  if  dwelling  index f i r s t  "floorspace"  of  a  the  specific  value a  convey  of  important  prominent  the  home  would  index.  to  relatively  play  The  ought  of  what  proxy  valuation  importance Thus  a  of  a  sense  the  relative  characteristics.  is  observed  in  determining  unit,  role  of  in  it  to  be the  should  also  establishing  the  value.  c r i t e r i o n  is  satisfied  by  any  vector  CJ  from  o equation second  4.1  which  c r i t e r i o n  is  may  constant be  met  by  across  dwelling  regressing  m(v  units. )  o  on  The  z  for o  the  69  hedonic  equation: m(v  )  a 'z  =  o The  u  resultant  in  4.1  to  OLS  o  estimates,  generate  +  a ' may o  values  for  x  o v  (4.2)  e  o then  .  be  used  Thus,  x  o which  would  appear  to  be  as  is  the  the  weights  value  of  o  consistent  with  the  observed  o characteristics  z  of  the  dwelling  unit.  That  is,  o m(x  )  =  E[m(v  )|z  o And  so  we  o  )  a'  =  o Although consistent  many  with  4.4,  a  )=log  for  example,  on  considerations:  in  uses  x  the  the  (2)  comparability  (3)  the  high  form,  of  semilog  equation  one  are  defines  with  other  computational  quadratic  Box-Cox  extreme present.  lack  literature.  form  interpreting  alternatives  at  hedonic  whereby  housing  preferred  the  the  ,  the  (1)  (4)  ease  of  o  frequently  (1980), four  (4.4) o  semilog  o most  z  o  specifications  m(x  found  (4.3)  have m(x  is  ] o  and  bases  his  choice  results; studies;  cost  of  based  functional of  Butler  consensus  the  upon  the  form, on  sometimes  and;  the  subject  70  Estimation table  I.  The  results  for  attributes  this  z  hedonic  are  defined  form in  are  reported  appendix  C,  in  and  are  o based  on  dwelling  supplied  by  variables dwelling the  unit  were  is  Life  which  situated,  from  characteristics  Survey.  census  thereby  These  1  electoral  allowing  of  the  principal  econometrics transform original described  the  the  data  components  program OLS  variables in  Judge  dummy  d i s t r i c t  location  the  to  m u l t i c o l l i n e a r i t y principal for  z  .  Then  o on  include  as  enter  d i r e c t l y .  problems  extracted  neighborhood  of  in  equation  avoid  and  Quality  indicating  hedonic To  the  unit  used  in  an  OLS  White  coefficients  back  to  et  §_1  in  (1985).  was  regression.  (see  reported  )  regressed  o  here  as  m(v  components  table  The  (1978))  is  able  correspond  to  the  I.  The  method  to  used  is  71  TABLE I Estimation Results for Hedonic Regressions VARIABLE* STREETS HOMES PARKS SCHOOLS SHOPPING SATISFCN BATHROOM BEDRM2 BEDRM3 BEDRM4 BEDRM5 BEDRM6 BEDRM7 SEMID ATTACH FLAT APTLT6 APTGT6 PARKING ZED506 ZED507 ZED508 ZED511 ZED515 ZED518 ZED525 ZED531 ZED544 ZED551 ZED553 ZED554 ZED560 ZED564 ZED565 ZED566 ZED574 ZED582 ZED583 ZED584 ZED585 ZED586 ZED587 ZED588 INTERCEPT Dependent v a r i a b l e : Adjusted R-square = 249 o b s e r v a t i o n s ; t *See appendix C f o r  COEFFS (T-STATS) - o . 8 0 0 E - 0 2 (-1 . 17 - o . 1 9 6 E -01 ( - 2 . 4 8 - o . 2 5 5 E - 01 ( - 4 . 2 3 - o . 2 2 1 E - 01 ( - 3 . 0 9 - o . 9 9 9 E - 0 2 (-1 . 4 5 + 0 . 2 0 2 E - 01 ( + 4 . 0 4 + 0 . 1 0 3 E + 0 0 ( + 12 . 5 -o. 1 3 8 E + 0 0 ( - 6 . 48 - o . 4 0 8 E - 01 ( - 2 . 6 7 + 0 . 7 2 1 E - 01 ( + 3 . 6 5 + 0. 2 0 7 E + 0 0 ( + 6 . 1 1 + 0 . 2 8 8 E + 0 0 ( + 5 . 41 - o . 1 5 6 E + 0 0 (-1 . 1 9 - 0 . 5 3 1 E - 01 ( - 2 . 7 3 - 0 . 157E+00 ( - 2 . 52 + 0 . 3 8 0 E + 0 0 ( + 3 . 91 - 0 . 1 8 6 E + 0 0 (-1 . 4 0 - o . 1 9 6 E + 0 0 ( - 3 . 17 + 0. 1 3 7 E + 0 0 ( + 5. 34 - o . 1 6 4 E + 0 0 (-1 . 6 3 + 0 8 2 6 E - 01 ( + 1 .1 1 - 0 . 1 9 7 E - 01 ( - 0 . 4 8 - 0 . 6 7 8 E - 01 ( - 2 . 5 2 + 0 . 1 6 7 E - 01 ( + 2 . 31 - 0 . 8 4 7 E - 01 (-1 . 0 7 + 0 . 2 9 0 E - 01 ( + 0 . 3 7 - 0 8 3 8 E - 01 (-1 . 3 0 -o. 2 2 3 E + 0 0 ( - 3 . 39 -o. 1 6 4 E + 0 0 ( - 3 . 44 - 0 . 220E+00 ( - 3 . 35 - o . 4 0 7 E - 01 ( - 0 . 91 + 0 . 3 3 5 E + 0 0 ( + 10 . 6 + 0. 6 0 4 E + 0 0 ( + 6 .62 + 0. 149E+00 (+0. 79 - o . 4 3 7 E - 01 ( - 0 . 8 8 - o . 7 0 1 E - 01 (-1 . 18 + 0. 1 8 7 E + 0 0 ( + 2 .37 + 0 . 2 4 5 E + 0 0 ( + 2 . 19 + 0. 1 8 5 E + 0 0 ( + 2 . 40 + 0 . 1 3 7 E - 01 ( + 0 . 4 9 + 0 . 3 8 6 E - 01 ( + 0 . 7 4 + 0 . 2 6 8 E - 01 ( + 0 . 4 0 + 0 . 4 8 6 E - 01 ( + 1 .0 3 + 0. 409E+01 (+59 .4 LOGVALUE .5715 F=15.382 r a t i o s r e p o r t e d w i t h 225 d e g r e e s of f u r t h e r d e f i n i t i o n of attributes  freedom  72  2.  Owner  occupied  Another quantity  of  the  dwelling  may  be  accommodation unit  worth  Several for  the  Rent to  used  those  is by  run  to  households  testing  were  sector,  but  the  dependent  for  the  owner  well  to  institutional  length  of  methods  tenure.  may  be  calculating  household  rental.  an  is  This  important  employed  did  not  variable  the  whether  distinction  one  produce in  a  and  is  for  the  for  rents  bit  of  provide  results.  rent;  a  estimates  similar  r e l a t i v e l y  rental  tendency a  usable  The  on  poses  equations  regression  restrictions  this to  hedonic  sector.  equations  possible While  estimate  occupied  hedonic  the  the  or  be  to  these  as  and/or  to  made  the  controls  by  when  for.  of  due  consider  occupied  performance be  accommodation  consumed  owner  attempts  rental  was  rental  characteristic  perceived  therefore  vs.  to  sector  x  may  namely  rent  depend  upon  problem,  of  poor  .  other  2  r One a  derived  together z  ,  in  method  which  from  hedonic  with  order  suggests  regressions  observed to  itself  is  for  characteristics  produce  estimates,  r  x  ,  to  the  the  owner  from of  use  the  the  coefficients  occupied rental  quantity  sector  sector, of  a  accommodation  services  which  the  vector  z  would  represent  were  r it  in  the  owner-occupied  sector.  That  is,  -1 x  =  m  (a'  a Another which  is  parameter, to  effect  u, the  z o  may  then  ) r  be  translation  introduced, from  the  the  rental  purpose  of  sector  to  the  73  owner  occupied Three  x  , x a  sector.  possible  and  s p e c i f i c a t i o n s f o r the  v are discussed  here.  They  relationship  between  are  r  x  =  ux  r log  x  =  v log x  r  has  been  - v  = x r  x  (4.5b) a  x  Once  (4.5a) a  (4. 5c)  a  calculated,  the corresponding  flow  price,  a may  be  p  , a  derived  directly  since  we  have  observations  on  rent;  that  is,  p  = R/x a  Similarly,  we  know  that  p  = R/x r  Thus,  using  equations  relationships  (4.6) a  between  (4.7) r  4.5 p  thru and  r  4.7  p  : a  we  may  derive  the  following  74  p  P r  (4.8a)  /v  a 1 -v x  P r  p a  a p  P  a  (4.8b)  x / ( x -u) a a  (4.8c)  r respectively. While  t h e demand  equation  f o rx  may b e d e r i v e d  ina  r straightforward resultant  fashion  expression  from  the indirect  i s stated  i n terms  utility  of x  function, the  and p r  which  of  r  i s observed. It  i snecessary therefore  equations  to substitute  4.5 a n d 4.8 i n o r d e r x  =  ( 1 - / 3 ) 7  r into  , neither  /3(e-7  +  a  variables  x a  so  the following;  x  (4.9)  r  a r e expressed i n terms  and p and i n terms a  =  ( 1 - / 3 ) 7  a  /  «  and p from r r t h e demand e q u a t i o n  )/p  c  new e q u a t i o n s w h i c h  yields  to translate  f o rx  +  /3(e-7  a  of the observed  o f t h e new p a r a m e t e r  Doing  (4.10a)  )/p  c  u.  a  ( 1 - u ) x  =  ( 1 - / 3 ) 7  a  x  +  0(e-7  a a  (4.1  )/p  c  Ob)  a  2 x  -  a  +/3(e-7  [ u + ( 1 - 0 ) 7  a  )/p  c  ]x  a  +  a  /3(e-7  ) u/p  c  a  = 0  (4.1Oc)  75  The  first  specification  of these x  =  ux  r is  quite  equations,  corresponding  , has t h e most  desirable  to the  properties.  It  a  similar  t o t h e demand  function  i n 4.9,  with  x  and  p  a substituted  for x  and p r  If owner  1,  v <  similar  rental  compelled  t o consume  in  t h e owner  sector  goods.  And  an  amount  so  v <  =  given  1 serves  (1-/3)7  1 The  more  to s h i f t  second  demand  log(x  equation  ) =  ulog(x  r explicitly  household  sector level  than of  non-housing  t h e demand  illustrated  share  curve  upwards  in figure  by  9.  third  i n 4.10,  corresponding  ), i s i n t r a c t a b l e .  to the  I t cannot  be  a  for x  unless a  The  of  the  than  a  specification  solved  as  case,  specified  i t s consumption  good"  otherwise  i n the rental  to derive a  (1-u)/u,  "lesser  they  In t h i s  housing  i n order  housing,  d  where  characteristics.  is  from  accommodation i s a  accommodation, even  observable  utility  respectively r  then  occupied  a  equation  7 =0 a  corresponds  or  /3=1.  t o the s p e c i f i c a t i o n  x  = r  -IJ.  x  The  demand  function  here  i s i n the form  of a quadratic  a equation  in x  , and  so  i t i s possible  to solve e x p l i c i t l y for  a two  distinct  and  offer  roots.  little  parameters.  However,  o r no  hope  of  these  solutions  retrieving  the  a r e most original  unwieldly  Theta S h i f t i n g Demand Curve  77  On  balance  therefore  the  first  specification,  x  =  ux  r the  best  test  choice  whether  among  households  characteristics would  in  the  the  in the  three  perceive rental  ownership  alternatives. a  given  sector  sector.  in  set the  a  It allows of  , is  us  to  housing  same  That  i s , we  can  has  arisen  over  , the  flow  light test  as  they  whether  u=1 .  D.  The A  Price great  measurement  of  Accomodation  deal and  of  controversy  definition  of  p  the  price  of  proper owner-  o occupied among p  .  housing.  housing  Yet  there  researchers  as  is a to  surprising  the  degree  appropriate  of  concensus  definition  of  Namely,  o  p  =  v  o where  v  o  i s the  e -IT ]  [w+r + X  (4.11)  g dwelling  unit  specific  stock  price  for  one  o hedonic  unit  rate,  i s the  r  of  owner  occupied  household's  housing,  opportunity  w  i s the  cost  of  effective  capital,  X  mill is  9 e the rate  gross of  rate  capital  Dougherty may  be  derived  of  p h y s i c a l d e p r e c i a t i o n and  gains and  Van  i n two  for  that  Order ways.  dwelling  (1982) As  a  i s the  expected  unit.  observe  "user  IT  that  cost",  this  p  flow  i s the  price  amount  o necessary  to  induce  a  household  to  give  up  one  unit  of  housing,  78  and  is derived  household's  from  utility  the  first  order  maximization  conditions  problem.  for  the  Alternatively,  p  may o  be  viewed  in  a  the  as  an  "implicit  competitive first  market.  order  maximization consumer's  agreement  problem,  the  and  the  rents  rental  for  the  which  price  may  landlord's  in equilibrium,  would be  prevail  derived  from  profit  i s equal  to  the  cost. recent  regarding  construction  This  conditions  user  While  rent",  of  p  literature  at  least  the  appears  to  be  appropriate  , a v a i l a b l e data  samples  largely  in  theoretical  have  not  yet  wholly  o conformed (1980), of can  new  to  the  this U.S.  to  housing. housing  it  Another  on  Jones  ignores  places  undue  and  nominal  on  alternative by  maintanence, this  opportunity  as  noted  emphasis  misperceptions  (1984),  the  example,  by  on  interest  Diamond  the  stock  rates,  and  as  to  the  true  cost  measure  of  the  flow  value  DeLeeuw  (1971),  taxes,  utilities  measure cost  of  in  fact  is  i s the and  seriously  capital  on  this  of of  sum  of  mortgages. flawed  the  price  DeLeeuw  Specifically, occupiers notation  the  total  provided as  =  measure  by  is  monthly  the  QOL  cost  survey  provided (TMC) may  by  owner's  the  variable be  QOL  data.  for  owner-  expressed  in  our  follows:  (1/12)V  x o o  [(1-G)r  +w+X m  ] m  As  because  equity.  The  TMC  For  s e r v i c e s , proposed  by  housing  units  serious  expenditures noted  CPI  dwelling  lead  view.  (4.12)  79  while  the opportunity  r  (1-e)r  =  cost  of c a p i t a l  f o r homeowners  i s given  + 0(1-t)r m  by  (4.13) b  where (1-0)  i s the proportion is  r  of the dwelling  unit's  value  which  mortgaged,  i s t h e mortgage  rate  of i n t e r e s t f o r the household,  m r  (1-t)  i s the a f t e r  tax rate  of return  the household  could  b expect  to receive  investment X  i s the value  from  bonds  or  other  income,  of maintanence expenditures  expressed  as a  m proportion t  Using  i s the household  equations  4.11  of dwelling  head's  through  unit  marginal  4.13,  value,  income  and  tax rate.  t h e r e l a t i o n s h i p between  p o  and  T M C c a n be  summarized  by e  p  where  =  12*TMC/X  o X = X - X . n g m In  other  annualized  +  words,  per unit  [0( 1 - t ) r + X - 7 r  v  o  o  b  the v a r i a b l e basis  is a  ]  (4.14)  n  T M C when  expressed  s u i t a b l e proxy  for p  on a n , once i t  o has  been  homeowner  adjusted equity  anticipated  f o r the opportunity as well  capital  as  gains.  cost  of c a p i t a l  f o r net physical  on  depreciation  and  80  The  QOL  mortgage study. 1979,  data  indebtedness With  this  t h e base An  provide  year  develop  using  Tobit  i s also  variable  implicit  As  by C h i n l o y  information  f o r 1977, t h e f i r s t  o n e may  adjustment  noted  explicit  (1980),  year  suitable  household  of the panel  estimates  of 0 f o r  regressions.  required  i n t h e QOL  on  f o r the  variable  TMC  the gross  depreciation  from  equation  depreciation  4.12.  rate  (X )  9 applied for  to the dwelling  total  depreciation  depreciation  and r e p a i r ,  by  through  identity  X =X g  The  do  +X n  QOL  i s the appropriate  costs  faced  by h o u s e h o l d s .  where  plus  these  by d w e l l i n g  Gross  expenditures  on  are a l l converted  unit  value,  measure  to  rates  yielding the  . m  variable  expenditures included  value  i s net depreciation  maintanence dividing  unit  TMC  encompasses  maintanence  but not net d e p r e c i a t i o n ,  explicitly,  so by n o t i n g  as i n equation  which  4.14.  and  must  repair  therefore  I t may  be p o s s i b l e  that e (Av/v)  e = TT - X  (4.15)  n  e since  IT  refers  depreciation dwelling  to capital  e f f e c t s while  unit  depreciation  would  gains  movement  reflect  effects.  n e t o f any  both  Thus  physical  i n the stock  capital  4.14 may  be  gains  price  and  of a  physical  rewritten: e  p  = o  12*TMC/x  [e(l-t)r  + v o  o  -(Av/v) b  ]  be  (4.16)  to  81  e It is  remains  perhaps  because  the  homeowners  QOL  most  are  of  survey),  estimates. This  a l l the  their  one  has  problem  example,  reliable  his the  but  cites  these  (1980),  .  problems  with  short  of  which  asking  regarding  units  was  not  (which  ground  upon  This  down e m p i r i c a l l y  are  lines  and  and  an  capital costs  and  to  price  other  refers  which  but  each  ignore  for  the  done to  the in  the  base  Van  Rosen  which  rental Order  capital  derives  homeowners  absence  expected  to  gains  an  from  expression  similar  to  our  in proceeding  (1979) and  (1982)  the  them.  He  price  in  in  homeowner's  exludes  serves  as  potentially  that  empirical difficulties  follows  researchers  expectations  states  variables. rate  housing  to  gains  consciously  rental  so  by  estimating  effective  Dougherty  (1979)  by  of  assumption  the  faced  user  too,  formidable  from  (Av/v)  expectations  firm  is forced  effective  invoking term  he  income  for  played  method  gains,  been  Rosen  perceived  both  dwelling  has  determining  King  pin  particular,  their  for  3  For  capital  In  little  role  a  v a r i a b l e to  measurement  fraught.  significant  of  suitable estimates  difficult  o u t r i g h t what  value  well.  develop  i t entails  expectations  future  to  Laidler  remove  the  (1969)  capital  own,  along by gains  expression. suggest,  and  this  researcher  e agrees,  that  expected longer term  to  rate  the be  the of  appropriate  rate  return  the  holding  over  period,  i n f l u e n c e d by  the  for  relevant  less  cyclical  (Av/v)  or  likely  i s the  holding  period.  is this  speculative  annualized The  expectations  fluctuations in  82  housing  stock  expectations differ  from  within  the  the  extent  "dwellers" time  be  a  only  those  therefore,  households  the  than  (1983)  long  periods  more  grossly sample. rates  the  i s not  housing  a  suggests five  gains  changes  in dwelling  QOL  on  or  capital  the  user  costs  may  operate  are  Thus,  to  as  expectations  particularly  in  the  stock  a  as  the  unit  real  early well  time  outlook  using  as  values  may  as be  as  houses  for  tended  to  rate.  estate  the  high  may  appreciate He  argues  as  a  markets  This  such  i s due  to  as the  transactions  housing.  horizon, of  period  This  rates  1980s.  most  some m e a s u r e  year  rates  advantageous  r e l a t e d to  longer  six  have  inflation  a  we  not  households  of  expected  proxy  modified  reported  may  by  be  in  our  inflation  for anticipated by  actual  respondents  to  survey.  definition  of  c o n s t r a i n t s on p  .  Jones  borrowing  (1984)  may  further  distinguishes  modify  between  o several  may  behaving  longer  inflation  in volatile  housing.  Institutional our  even  applying  This  a  distant  horizons.  appreciation  than  considerations  by  time  in general,  quickly  misrepresenting  over  that,  houses  in Vancouver  Thus,  who  sample  time  those  tax  our  of  housing  of  short  in  expected  vehicle  illiquidity  resulting  "speculators",  argues  speculative found  relatively  appropriate.  i n d i c a t o r of  that  the  relatively  as  a  speculators  that  Capozza  and  by  of  slightly  costs  choose  confines  rather  over  we  perceived  is  further  If  horizon,  horizon  good  since  prices.  classes  of  homeowners,  based  on  their  debt/equity  83  ratios. whose cost  One  net of  of  worth  the  observed  of  being  the  influencing  the  anticipated inflation,  class  to p  of  amounts  and  the  tenure  example,  prototype small  acquired.  relationships  services  For  i s the  relatively  for this  determinants  housing  is a  house  constraints  on  these  most  T h i s may  the  the  as  capital  borrowing  likely  q u a n t i t y demanded,  to  have  be  a  the  bearing  owner-occupied well  as  itself.  housing  become  are  of  a p p r e c i a t e more can  homebuyer',  that  price  choice  where  argues  borrowed.  between  time  p r o p o r t i o n of  He  owner  'first  quite  stock  values  rapidly  than  low  or  even  are the  widely general  rate  of  negative,  o Institutional behavior  of  negligible  constraints  households c o s t s of  Dougherty Kearl's  (1979)  borrowing capital  and  who  borrowing  rent  Van  Order  flow  the  a  additional  explain  the  seemingly  that,  constraint  f o r the  to  services.  observe  constraint,  help  f a c e of  housing  (1982)  expression  t o c o n t a i n an  would  i n the  owner-occupied  cash  causes  on  user  cost  similar  to  on  total  of  housing  term: e  p  = v o  where  c  i s the  constraint  to  ratio the  o of  - 7 r +c]  [w+r + X  the  marginal  (4.17)  g shadow utility  price of  x  of  the  , the  borrowing  nonhousing  good.  c (Note  that  c  drops  Intuitively,  out this  when  the  revised  constraint expression  is  nonbinding.)  suggests  a  e "counterbalance"  to  the  tendency  f o r ir  to  pull  the  flow  price  84  of  owner  occupied  is  correct,  term  'c'  with  little  applies  we  to  would  user net  costs worth  for  discussion  thus  of  as  rental  determine.  In  our  units  i s the  dwelling capital  unit, gains,  landlords, of  E.  rental  who  =  Three  permanent savings,  monthly  ie,  stock  on  the  a  those  values.  housing  occupied  This  markets.  price  of  dwelling units.  The  straightforward to  household  we  have (4.18)  cost  reported  of by  residing the  QOL  d e p r e c i a t i o n and  the  are  here,  not  modelled who  i n the  respondent's  survey.  like  are  Considerations the  rather  concern  than  of  of  the  of  the  tenants  are.  Expenditure  data  versus and  buyers,  add  r  issues arise  expenditure  home  12*R/x  accommodation,  Defining  i f we  focused  f o r each  hypothesis  improve  housing  owner  Jones'  to  i s c o n s i d e r a b l y more  particular,  as  If  inflationary  f a r has  r R  time  to  highly  far".  results  first  p e r t a i n s to  p  where  "too  relative to  accommodation  down  expect  particularly  The  price  housing  (3)  from  regarding  the  current  QOL  use  survey.  income  implicit  the  of  They  measures,  expenditures  household are  (2)  on  (1)  the  owner  the  role  use  of  of  occupied  housing. Most are in  not the  an  authors  adequate  context  durables."  agree  of  that  measure  the  current period expenditures of  demand  Theoretically,  one  expenditure  for housing should  use  or  or  income  other  when  alone viewed  major  anticipated  household  85  earnings  over  (1974).  However,  QOL  survey.  household The  As  expected  second  proxy after  system  housing  of  (x  tenure,  therefore this taxes  reported  5  the  model  total  expenditure  = p  x o  well,  of  savings.  is a  complete  between (x  1977,  the two  ).  in in  Muth the  average and The  1981.  6  linear  system  of  household's alternatives,  By  definition  c  e  As  1979,  i s , i t describes  consumables  reported  in  That  other  not  outlined  uses  in this  expenditure  as  research  role  a therefore,  are  used  total  ) and  of  earnings  issue concerns  equations.  allocation  length  anticipated  a  income  expenditure demand  the  total  (e)  +  x  o  expenditure  satisfies  (4.19) c  may  be  defined  as  net  income  (y)  less  savings;  e  A not  slight  provide  =  problem  explicit  y  -  s  (4.20)  arises data  in that  on  either  the s,  panel  x  , or  data e;  used  here  do  although  c information We total just  are  on  net  compelled  expenditure. another  expenditure  income  good,  (y)  is  provided.  therefore to  This  use  is equivalent  distinguished only  is actually  net  made  7  since,  to by  by  income viewing  the 4.19  as  proxy  'savings'  period and  a  i n which  4.20,  we  for as the  have  86  y = p x + ( x + s ) o o c  This  i s less  average one  of  over  year A  a  problem  several  will  final  tend  years,  to  on  the  ) of  i s d e f i n e d as  i s the  here.  case  dissavings in  needs  housing.  expenditure  as  offset  adjustment  expenditures  when  (4.21)  to  be  Recall  made  from  savings  in  another.  for  the  For  an  implicit  previous  section  that e  price  (p  owner  occupied  housing  has  an  explicit  (p  o  ) o  i and  an  implicit  (p  )  component.  The  former  includes  cash  o disbursements latter  mortgage  includes implicit  capital on  on  the  on  homeowner  home.  Thus,  payments, costs  such  e q u i t y and 4.19  may  e  =  o net  However,  y  =  [(p  income  as  opportunity  the  negative  rewritten  maintanence.  of)  cost  capital  f o r homeowner  8  The of  gains as  i  )  o (y  and  (the  be  e  taxes,  +  (p  )  ]*x  o ) from  the  o QOL  +  x  (4.22)  c survey  i s given  by  Q  y  =  e ) x  (p  Q  o  It  i s necessary  (p  )  + x o  (4.23) c  therefore to  add  implicit  housing  expenditures  i ]*x  o be  to  net  income  reported  i n the  QOL  survey  before  i t can  o used  above.  9  as  a  proxy  for expenditures  in the  manner  described  87  NOTES  TO C H A P T E R  FOUR  1.  Several hedonic r e g r e s s i o n s were r u n u s i n g s e v e r a l s e t s of attributes. The r e s u l t s r e p o r t e d t a b l e I a r e t h o s e which were j u d g e d by t h e a u t h o r t o y i e l d t h e b e s t c o m b i n a t i o n of o v e r a l l f i t and s e n s i b l e i n t e r p r e t a t i o n .  2.  Rent c o n t r o l s were i m p l e m e n t e d i n O n t a r i o e f f e c t i v e J u l y 1975, and so had been i n e f f e c t f o r f o u r y e a r s p r i o r t o our base year.  3.  E v e n t h e n , one must r e c o n c i l e t h e s e the views of p r o s p e c t i v e buyers.  4.  F o r e x a m p l e , most o f t h e p a p e r s r e v i e w e d by Mayo (1981) u s e an a v e r a g e o f r e p o r t e d i n c o m e s o v e r s e v e r a l y e a r s a s a proxy f o r "permanent income". That i s s i m i l a r t o the approach taken here.  5.  C a n a d i a n income t a x forms f o r t h e a p p r o p r i a t e y e a r s were used t o c a l c u l a t e the r e l e v a n t deductions and t a x r a t e s .  6.  I f o b s e r v a t i o n s a r e l a c k i n g f o r one of t h e s e y e a r s , t h e e s t i m a t e o f h o u s e h o l d income i s b a s e d on t h e r e m a i n i n g years. C h i l d r e n ' s income i s n o t i n c l u d e d .  7.  This i s consistent with the i m p l i c i t intertemporal separability discussed  8.  Setting  9.  A c t u a l l y , these net i m p l i c i t expenditures n e g a t i v e due t o c a p i t a l gains.  savings  (s) equal  to  owner  expectations  assumption i n chapter  o f weak two.  zero. are  typically  with  88  V.  E s t i m a t i o n and  Results  A.  Summary  Basic  For  of  ease  summarized  of  by  likelihood  the  Model  r e f e r e n c e , the  equations  5.1  full  through  model 5.4,  from  beginning  L  three  with  the  is  log-  function h  log  chapter  =  [Z  = Lt  h  Z j  d  +  Ld.  *logP  j  h ] +  [Z  j  Z h m m  d  *logf  (e ) ] m m (5.1)  h=(1,H) j=o,r,s m=o, The  first  term,  r  L t , embodies  a  g e n e r a l i z e d extreme  value  h (GEV)  model.  I t d e s c r i b e s the  probability  (P  ) of  household  h  j selecting  tenure  j as  a  function  of  i t s expected  utility  in  h tenure  (A  )  relative  to  the  alternatives.  That i s ;  1  j  a  h P  =  exp[A  m  /(l-a)]*M  /D  (5.2a)  m h  P  = s  where  exp[A  ]/D s  (5.2b)  that  89  h M  = exp[A  /(1-a)]  +  exp[A  o  /(1-a)]  (5.2c)  r  h  1-a  D  = exp[A  ] + M  (5.2d)  s  As  described  an  LES  i n chapter  specification.  three,  these u t i l i t y  levels  are  based  Thus,  h A  = b(/3)  l n ( e -p 7 - 7 ) m m a c  +  m  |31np  -  K  (5.3a)  m for  m=o,r  h A  01n(x -7 ) s a  = s The  second  functions demand  ( s =p m  h m  = m  (e  h )  expression  f o r the error  share  f  (1-/5)ln(x  +  x ) mm  (2;ra  2-1/2 )  = E(s  ) -  -7 ) c c  i n 5.1  terms  (5.3b)  comprises the  from  density  the households'  conditional  equations;  2 exp[-e  2 /2a m m  ]  (5.4a)  where  m =  [p  s m  m  (1-0)7  +  m Equation parameters  a 5.1  0(e  -7 )]/e m c  i s maximized  appearing  with  s  (5.4b) m  respect  i n e q u a t i o n s 5.2  to the  through  5.4.  six  basic  They  are  on  90  the  marginal to  a  share  of  which  goes  housing,  perceptual  parameter  accommodation occupied  —  household expenditures  parameters  from  a  measure  of  a  parameter  correlation moving  prices  into  model  which  serve  f o r accommodation  owner-  to  services  and  respectively,  the d i s u t i l i t y  from  and  rental  units,  t h e LES  the axes  goods,  translates  quantities  measurement  translate other  which  t h e GEV between  options  of  model error  (m=o,r).  residential  which terms  allows  relocation,  for  f o r the  two  91  B.  Nonlinear The  5.4  Estimation  likelihood  i s clearly  nonlinear Newton  function  nonlinear  estimation  method  Fletcher(1970,1972). Vaessen(1984). derivatives.  3  based  The user  For this  may  Variables  1.  Demographic  scaling  complete  demand  Pollak  and Wales  ch.8).  Of t h e s e  translating  replacing  employ  ways  numeric  to introduce  s y s t e m s , a number (1981)  procedures,  a l lquantities  through  quasi-  i s found i n  numeric  or  analytic were  used."  translating  demographic  variables  are discussed  and Muellbauer  demographic  scaling  into  by  (1980,  and demographic  interest . 5  modifies x  a  by  derivatives  of which  a n d by D e a t o n  scaling  5.1  employs  described  either  and demographic  are of p a r t i c u l a r  Demographic  research  on p r o g r a m s  research,  Demographic  a r e many  This  The d o c u m e n t a t i o n f o r FLETCH  C.  There  by e q u a t i o n s  i n parameters, and so c a l l s f o r  techniques.  (FLETCH)  2  summarized  from  the o r i g i n a l the o r i g i n a l  demand utility  s y s t e m by function  i U*  by t h e i r  respective  U(x)  In  order  in  an i n v e r s e  scaled  values,  x /m . i i  Thati s ,  = U*(x/m)  to satisfy  t h e budget  manner;  (5.5a)  constraint,  prices  must  be  scaled  92  V(p,e)  with  = V*(pm,e)  (5.5b)  t h e c o r r e s p o n d i n g demand  functions  given  by  x(p,e)=mx*(pm,e) i i i These Barten  scaled  (1964)  variables. Barten into  as  To  based  typically  vehicle  and  prices  i f m  capita  general  may  employs  consumption of  f o r each  translating, translation  size,  transforms the  function  differ  first  then  by  the  demand  levels.  the  proposed  demographic  i s household  on  per  were  for introducing  effectively  Demographic (1978),  a  and  method  a more  variables,  quantities  illustrate,  scaling  one  (5.5c)  system  However,  pertinent  m  is  demographic  good.  first  applied  parameters  by  (t ) to i  Pollak shift  and the  Wales axes.  Thus, U(x)  =  U*(x-t)  V(p,e)  (5.6a)  = V*(p,e-I p t i i i  )  (5.6b)  and x  (p,e)  =  x*  i where  the  (p,e-Z i  t  are  some  p i  t i  functions  ) + i of  t  (5.6c) i  household  characteristics,  i The  similar  demographic  to  the  translating  translating  parameters  parameters  (7  (t ) are i  ) found  quite  i n the  LES  i specification  discussed  in chapter three.  Indeed,  demographic  93  translating  is applied  to  the  LES  model  by  simply  replacing  7 i  with  7  +t i  i n e q u a t i o n s 5.3  translation household For  parameters  and  is  employed  2.  Initial  obtain  model,  here  virtue  of  this  LES  model  become  be  shown  that  deal  of  technique  the  functions  of  either  converging,  or  7  the  effort with  final  was  the  (i=a,c).  pages,  7  .  However,  neither  parameter  basic  procedure  estimates.  to  in early  model,  Throughout  stalled  source  demographic  equivalent  expended  A l l attempts  bombed  frequent  following  the  attempts  translating.  success.  parameters  procedures are  to obtain  convergence  procedure  i t can  i n the  estimation  good  of  A  LES  explained  demographic hints  By  i n the  translating  reasons  A  .  characteristics. the  scaling for  6  i  this  run  to violation  of  problems  These  with  period,  the  at meaningless  due  both  were  parameters  and  8  LES  enter  were  estimation  conditions.  translation the  LES  model  1  embedded  within  restrictions  logarithms,  implying  (see e q u a t i o n s  e  m  7  x s  c  parameter  -7 a  > 0  (5.7a)  c  > 0  (5.7b)  > 0  (5.7c)  a  7  X  following  5.3):  7  p m  the  c  no  without  regularity  the  to  without  there  nonlinear  values of  attempts  94  The  estimation  r o u t i n e f r e q u e n t l y produced  estimates  7  of  and c  7  which  violated  these  restrictions,  thereby  causing  the  a estimation  process  efforts  i n t r o d u c e demographic  to  One  indirect  h  abort.  This  problem  of  the  subutility  expressions  indexes  exacerbated  this  problem  i n 5.7,  so  by  i s to  that  use  the  linear  direct  and  become  = b(/3) + l n ( e ) - ( p 7 +7 ) / e  m  was  translating.  strategy for dealing with  approximations  A  to  m  a  c  - 01np  m  K  -  (5.8a)  m  and h  A  = ^ l n x - 7 /x )  s This  s  convergent These  of  first  has  The  second where  driven  by  purely  solutions While  In  only)  almost  estimates  are  and  5.8a  and  5.8b  model  choice  in appendix  strategy provided  solutions,  for  considerations.  reviewed  second  a  i t i s not are  no  distinct  reasonably  with  /3 i s q u i t e  high  of  "demographic  selection These  is  two  D.  welcome  relief  entirely  longer  values.  interpretations.  accord  estimate  tenure  two  likelihood  different which  7's.  the  uncovered  suggests  the  demographic  convergent  particular,  0=0  briefly  this  the  solution  on  identical  intriguingly  parameter  determinism",  of  (logit with  have  restrictions  expectations, although  0.64.  form  5.8  solutions  solutions  priori at  (5.8b)  s  f o r m u l a t i o n p l a c e s no Estimation  The  a  dual  in  the  satisfactory. to  one  another.  a  95  Instead,  they  Moreover, into  5.3  substituting causes  regularity  fall  does  a majority  short It  was  estimated  specified  reported  for j  7  and a  and  7  *=-1000)  were  values  the linear  form  Thus,  approximation  the  values  f o r t h e LES solutions  chapter.  a ceiling  ceilings  used  on t h e here  c  arrived  i n 5.3.  the  in this  The  from  forms  f o r the l i n e a r  to place  .  dual  to violate  starter  later  therefore necessary  values  i n 5.7.  useful  the l i k e l i h o o d  of those  values  of households  not generate  Finally,  of the t r u e  the solution  conditions  procedure model.  are approximations  (7  *=0 a  at through  a  simple  grid  search  c procedure,  varying  7  by  increments  1 and  of  7  a 1000.  The  7  = i  where  r  model  was  then  re-estimated  increments  using  7 * - exp(T ) i i i s t h e new  by c  i=c,h  parameter  t o be  estimated.  (5.9)  Ina l l  i instances,  the values  for T  were  large  and n e g a t i v e  so  that  i exp(r  ) became  indistinct  from  zero.  Therefore,  i fixed  the 7  were i  at 7 * f o r the f i n a l i  estimation.  9  of  96  3.  Demographic The  focuses  use  variables  and  of demographic  upon  the  LES  tenure  choice  translating  within  parameters, 7  translation  an  LES  framework  .  This  has  i worked  well  for Pollak  context  of  complete  goods.  These  decision.  introduced  parameter  earlier  t h e manner  which by  reasons  f o r wanting  family  willingness For sample years  of  to  of  relocation,  This  have  They  marital  are  K , the to  be  specification  various sociodemographic to  relocate.  versus confirm  status  Simple  demographic that  age  attributes  of h o u s e h o l d  are correlated  below  versus  been  married  the  31  while  with  107  Likewise,  of  the  well  had  the 17  ten years. been  that  above  sample,  of  than  demarcation in  in the  42  stayers as  movers only  for less  appear  disutility  h o u s e h o l d heads  forty-three.  would  variables  allowing  choice  tenure  for  by  a  than  It  in order  is offered  t o be  Of  married  be  the  choice.  wanting)  II.  consmer  t o model  appears  forty-three,  71  and  there  than  the  tenure  i n the  a  relocate.  example  of age.  (or not  others  demographic  variables.  in table  size,  between  the  seek  therefore  tenure  h o u s e h o l d s may  crosstabulations  head,  of  means  demographic  summarized  may  and  for non-durable  d i d not  i n which  measures  that  (1978)  systems  efforts  i n the context  recognizes  are  demand  straightforward  modified  Wales  Some a d a p t a t i o n s  respecifying  A  and  married  moving  forty-three  26  were  stayers  married  In c o n t r a s t ,  i s more  younger  were  movers,  for less  this  younger 16  only  than  disruptive  had 13  ten for  of  years.  TABLE  II  C r o s s t a b u l a t i o n s of R e s i d e n t i a l M o b i l i t y and S e l e c t e d Demographic A t t r i b u t e s  Movers  Age  How  of < >  Head 43 y e a r s 43 y e a r s  Long M a r r i e d < 10 y e a r s > 10 y e a r s  Family Size < 4 > 4  Stayers  26 5  42 65  16 1  13 58  22 9  64 43  98  larger only  families.  9 were Based  Of  movers.  t h e 52  with  four  o r more  members,  1 0  on these  /c(d) =  families  findings,  6 + k  5 d + k l 1  K was r e p l a c e d  6  d + kw w  5  in  5.3a by  d kn n  (5.10)  where d  =1  i f age of household  head  i s less  than  43,  1 otherwise,  d  =0 1  d  =1  i f the household  head  i s married  and has  w been  d  for less  than  i s household  10 y e a r s ,  otherwise,  d =0; a n d w  size,  n When  K i s replaced  variables  d  influence  by « ( d ) i n 5 . 3 a , t h e d e m o g r a p h i c the tenure  decision  but not the  i conditional  demand  expect  the marginal  that  accommodation To  test  might  decision. share  However,  of expenditures  be i n f l u e n c e d  for this  i t i s not unreasonable  possibility  toward  by f a m i l y  size.  directly,  /3 i s m o d i f i e d a s  well;  /3(d)  = 5 b  Estimation  results  hypothesis  that  5 bn  + 5 d bn n  (5.11)  r e p o r t e d below =0.  This  may  cannot  reject  be p a r t l y  the null  e x p l a i n e d by t h e  to  99  fact  that  x  i s a hedonic  measure  of accommodation  services  a consumed. behind For  A number  this  hedonic  example,  prestigous  of tradeoffs veil  a larger  location  which  family  b e made  by  households  are not captured  may  i n favor  may  choose  by t h e d a t a .  to reside  of a dwelling  unit  in a  with  less  more  bedrooms.  D.  1.  Results  Disutility Table  described  III presents above.  conditions is the  robust  point  central  generally  to transactions of t h i s  demographic  results  satisfies  f o r t h e model  the second  of the l i k e l i h o o d  order  f u n c t i o n , and  i n the starter values  used  during  process.  are several  most  relocation  extent  solution  to a r b i t r a r y changes  estimation  Perhaps  This  ( K )  the estimation  f o r a maximum  There  due  of Relocation  interesting features  to this  model  results  in significant  costs  utility  status.  This  i s the finding  and uprooting  loss  is clearly  i s shown  of these  that  household  effects. a  results.  disutility  Moreover, the  function  by t h e v a l u e s  of household f o r the 6 k  reported  i n table  confidence larger  I I I , which  levels.  1  1  Perceived  f a m i l i e s , but a r e lower  newlyweds.  This  probabilities,  has a d i r e c t  as w i l l  a t 95  are a l l significant  be s e e n  transactions f o r younger effect  costs  shortly.  are higher f o r  f a m i l i e s and  on t e n u r e  percent  choice  100  TABLE I I I Maximum L i k e l i h o o d P a r a m e t e r Estimates f o r the F u l l Model 1  Parameter  0 8  Estimated Value  Asymptotic t-stat  .19084  10.49  2.5494  3.61  -2.5473  -3.57  -1.5479  -2.78  0.5699  2.66  k 8 kl 5 kw 8 kn  log  L  -47.6583  1. The f o l l o w i n g p a r a m e t e r v a l u e s were h e l d f i x e d d u r i n g this e s t i m a t i o n ; v = 1.0, y - 0, y = - 1 0 0 0 , a = 0. See t e x t f o r a c details.  101  As  described  function  to  For  =  the  given  e  or  equivalent  ( p ,A m m m  LES  moving  )  model  -  e(p  two, costs  can  in  in  =  e  use  terms  transactions  , A -K) m m  outlined  one  e(p  the  expenditure  foregone (TC).  That  ,A - K ) m m  m 5.3a,  of  costs  -  the  u t i l i t y  is,  (5.12)  for  a  mover  is  by  A  =  b(/3)  +  ln(e  - p 7 -7 ) m m a c  m So  chapter  calculate  expenditures TC  in  by  -  |31np  -  K  m  d e f i n i t i o n ,  e  =  e  (p ,A ) m m m  G  =  m  =  exp(G+«)+g  (5.13)  where A  +/31n(p m  )-b(0) m  and g  Combining  =  p  5.12  transactions TC  =  7 m a  +  7  and  5.13  terms  exp(G+«)  c  i t  is  now  to  solve  for  the  e x p l i c i t y ; -  exp(G)  =  exp(G+/c)*[ 1 -exp(-/c) ]  =  (e  -g)*[  possible  1-exp(-/c) ]  (5.14)  m As  shown  exp(-K)]  vary  considered four  with  married  in  widely  here, a  for  table  the  household at  least  IV,  by  values  household  least head ten  the  likely aged  years.  for  type. to  the Of  In  the  relocate  forty-three  expression  is  or  contrast,  eight a  more a  [1-  prototypes  family who  young  of  has  been  newlywed  1 02 TABLE I V T r a n s c a t i o n s Costs (TC) a s a P r o p o r t i o n o f R e s i d u a l Household Income (e -g) f o r E i g h t H o u s e h o l d Prototypes m Household Characteristics*  T C / ( e -g) m  L E 4 2 == 0 NWED == 0 NHSD == 2  0.975  L E 4 2 == 1 NWED == 0 NHSD == 2  0.681  L E 4 2 == 0 NWED =• 1 NHSD == 2  0.882  L E 4 2 == 1 NWED == 1 NHSD == 2  -0.501  L E 4 2 == 0 NWED == 0 NHSD == 4  0.992  L E 4 2 == 1 NWED == 0 NHSD =• 4  0.898  L E 4 2 == 0 NWED == 1 NHSD == 4  0.962  L E 4 2 == 1 NWED == 1 NHSD == 4  0.520  •Definitions: LE42=1 i f h e a d i s y o u n g e r t h a n 4 2 , L E 4 2 = 0 o t h e r w i s e NWED=1 i f m a r r i e d l e s s t h a n 10 y e a r s , NWED=0 o t h e r w i s e NHSD e q u a l s s i z e o f h o u s e h o l d  1 03  couple These  without  The  dominant  strong  variables  choice  probabilities IV.  25 p e r c e n t  excess  findings demand lower  results  that  Table  eight  family  of four  o f 98 p e r c e n t . of S t e e l e  i n Canada,  1 3  (1979, reports  variables are  1 2  of moving  V presents  household  t h e young  period  This  f o r i n t e r p r e t i n g the e f f e c t of  p r o b a b i l i t y of staying  (two-year)  large  i n our sample.  demographic  the d i s u t i l i t y  f o r t h e same  IV a r e q u i t e  observed  decision.  context on  by t a b l e  that  probabilities.  I t shows  established in  relocate.  the crosstabulation  levels  evidence  meaningful  demographic  one  implied  i n the move-stay  A more  table  o f TC  to the expenditure  constitutes  tenure  with  to  earlier. values  relative  from  i s positively inclined  results are consistent  reported  a  children  in their  t o the next.  on  these  types  newlywed  i s based  considered  couple  has  current  less  in than  residence  In c o n t r a s t ,  the w e l l -  has a p r o b a b i l i t y of not r e l o c a t i n g These  results are consistent  p 1 6 ) who, that  i n her study  "greater  p r o b a b i l i t y of r e l o c a t i o n .  age  of  with  the  housing  i s associated  with  a  TABLE V o  COMPARATIVE HOUSEHOLD CHARACTERISTICS AND TENURE PROBABILITIES AT MEAN PRICE AND EXPENDITURE VALUES  HSHD CHARS  O W N E R S  R E N T E R S  A L L  PROB THAT TENURE = M/OWN M/RENT STAY  PROB THAT TENURE = M/OWN M/RENT STAY  H S H D S  PROB THAT TENURE = M/OWN M/RENT STAY  LE42 = O NWED 3 0 NHSO S 2  0.025  0.022  0.953  0.026  0.024  0.950  0.025  0.023  0.952  LE42 = 1 NWED 0 NHSD = 2  0.202  0.183  0.614  0.211  0.191  0.598  0.205  0.186  0.609  LE42 = 0 NWED = 1 NHSD 2  0.099  0.089  0.812  0.104  0.094  0.802  0.100  0.091  0.809  LE42 1 NWED = 1 NHSD = 2  0.392  0.355  0.253  0.399  0.361  0.240  0.394  0.357  0.249  LE42 = 0 NWEO = 0 NHSD = 4  O.OOS  0.0O7  0.985  0.009  0.008  0.983  0008  0.008  0.984  LE42 = 1 NWED O NHSD = 4  0.088  0.079  0.833  0.093  0.084  0.823  0.089  0.081  0.830  LE42 = 0 NWED = 1 NHSD 4  0.036  0.033  0.931  0.039  0.035  0.927  0.037  0.033  0.930  LE42 = 1 NWED St 1 NHSD 3 4  0.255  0.231  0.515  0.264  0.239  0.497  0.258  0.233  0.509  1 05  2.  Expenditure  and P r i c e  The e x p e n d i t u r e outlined  and p r i c e  above a r e g i v e n  r e s p e c t i v e l y by  (5.15a)  r?(p)  = -/3(e-7  (5.15b)  ) / [ p (1-/3)7 +/3(e-7 ) ] a a c  i n t h i s chapter,  on t h e e s t i m a t e d  7  substituting  = /3e /  to place  f o r 7 a n d 7 , so t h a t a c  = 7 * - exp(r ) a a  (5.16a)  = 7 * - exp(r ) c c  (5.16b)  c  f o r 7 and 7 f r o m 5.16, t h e e l a s t i c i t i e s i n a c  5.15 may be r e w r i t t e n  •qie)  values  i t was n e c e s s a r y  a 7  as  [p O - / 3 H 7 *-expr a  i?(p)  f o r t h e LES model  = /3e / [ p (1-/3)7 +/3(e-7 ) ] a a c  As d i s c u s s e d e a r l i e r  By  elasticities  r?(e)  c  ceilings  Elasticities  a  = |3(e-7 +expr ) / c c  ) + /3(e-7 *+expr  a [p a  c  ) ] (5.17a)  c  (1-/3) ( 7 * - e x p r ) + /3(e~7 * + e x p r ) ] a a c c (5.17b)  It  i sclear  from i n s p e c t i o n  5.16 do n o t impose a p r i o r i  that  t h e r e s t r i c t i o n s imposed by  any r e s t r i c t i o n s on t h e s i g n s o r  magnitudes of t h e e x p e n d i t u r e  and p r i c e  elasticities  i n 5.17.  1 06  However, held  with  as  reported  equality,  so  7  earlier,  =  7  =  direct  price  r e s u l t of  =  *  0  =  the  (5.18a)  -1000  (5.18b)  elasticities  r/(e)  =  e  r?(p)  =  -1  /  in  5.15  now  become  (e+1000)  (5.19a) (5.19b)  elasticity the  is particularly  finding  7  that  =0.  striking,  That  i s , 7  a 7?(p)=-1,  regardless  of  the  values  of  are  unable  to  reject  the  null  and  =0  is  a  implies  a p  ,e,/3,  or  7  a we  5.16  c  consequence,  unitary  *  7  c  The  in  a  7  a  restrictions  that  a  As  both  .  Thus,  since  c  hypothesis  that  exp(r  )=0,  we  a are  also  unable  to  reject  the  hypothesis  of  unitary  price  ),  and  so  of  the  expenditure  elasticity. And  given  7  =0,  77(e)  e/(e~7  becomes  a p  has  any  effect  neither  /3  nor  c on  the  estimated  value  a elasticity.  Both  e  and  7  are  reported  in  units  of  annual  c expenditure  dollars,  so  7  =-1000  in  5.18b  ensures  that  the  c expenditure  elasticity  lies  between  0.9  and  unity  for  households  1 07  with  annual These  demand  expenditures results  has  been  housing and  are consistent  elasticities  Quigley(1979),  i n excess  as summarized  and M a y o ( l 9 8 l ) .  reached,  of  $9000.  with by  the evidence  inelastic  To t h e e x t e n t  with  housing  DeLeeuw(1971),  i t i s g e n e r a l l y agreed  i s slightly  on  that  respect  that  a  consensus  t h e demand f o r  t o both  expenditure  price. However,  using  a  log-linear  x a  e their  model  provides  are similar  useful  particular, of tenure  behavior,  elasticities  equation;  e  (5.20)  and p r i c e  elasticities,  choice  elasticity  First, They  conditional  model  in this play  a  demand  examines  and c o n d i t i o n a l  framework  and demographic Each  to those  reported here, earlier  this  estimates  features.  (b) t h e key r o l e  stayers.  reported  their  c o n f i r m a t i o n of those  this  defined  and  disutilities  duty.  demand  are the expenditure  results  consistently  from  housing  i t sd i s t i n g u i s h i n g  In nature  studies estimate  p  While  because  such  ( p ,e) = TJ I n e + rj l n p + a e p a  a n d TJ  77  where  most  demand  of household played  simultaneous  within  utility  a  maximizing  by t r a n s a c t i o n s  variables  of these  (a) t h e  in delineating  f e a t u r e s may  impact  upon  movers the  estimates. model  the parameters  key r o l e  i n both  decisions.  Those  are consigned  the tenure  choice  s t u d i e s which  to  double  and  examine  the  1 08  latter  decision  parameter  in isolation,  and e l a s t i c i t y  therefore,  estimates,  may  be p r o d u c i n g  as suggested  biased  by L e e a n d  Trost(1978). The  second  major  feature  bulk  of e a r l i e r  role  played  by  that  models  by K i n g ( l 9 8 0 ) ,  this  barrier  the  true  prices  studies  typical demand  on h o u s i n g  transactions  elasticities. will  household, response  While  1  most  not l i k e l y  thus  giving  studies  of housing  which  have  Polinsky  and Ellwood  confined  their  regarding would lies  sample  a r e more  future  otherwise i n the risk  information and  this  the  limited  recently  to  small  overlook  understate  changes i n  o f an  do  inelastic  of sample  of information  and Kawai  sample  to  both  (1982)  levels  current  and demographic  A disadvantage bias.  one c o n s i d e r s may  their  For example,  consumption  selectivity  when  limit  consider  mover/owners.  to reflect  income  be t h e c a s e .  do n o t  relocated.  housing  likely  prices,  sample.  some  to recent  i s discarded  body  which  two  in relocation for a  demand  ( 1 9 7 9 ) a n d Goodman  so, current  sample  i s the  ".  households  their  result  tend  the appearance  barriers explicitly,  doing  i s that  from t h e  i n chapter  and o t h e r s  relocation will  The r e a s o n  model  elasticities  I t i s argued  Rosen(l979)  relocation  By  demand  costs.  to residential  o r income  distinguishing this  n o t be  expectations variables  in their A only  within  good  method deal  recent  faithfully  than  of  movers,  reflected  in  109  This  contrasts  bases  i t s parameter  using  transactions  attributes  to  with  the  method  estimates costs  highlight  as the  on  used  movers  modified  in  this  and  by  study,  nonmovers  household  differences  between  which  alike,  demographic  these  two  groups.  3.  Rental As  versus  Owned  described  Accomodation  in chapter  four,  (v)  the  perceived  differences  identical  units  in different sectors.  extent  to  which  a  rental  sector  similar  i n accommodation  bundle  of  is equivalent,  bundle  of  parameter  housing in  services That  v  measures  flowing  from  i s , v measures  characteristics in  the  eyes  c h a r a c t e r i s t i c s found  of in  the the  the  the  consumer,  to  a  owner-occupied  sector;  x  =  ux  r If  v equals  services and  not  on on  decision price,  one, the the  to  quite  basis sector  own  or  income,  Testing  then  and  of  were  significantly  Thus,  of  the  the  must  model the  be  reside.  explained  In  with  this  case,  reference  the  to  considerations.  shows value  accommodation  c h a r a c t e r i s t i c s themselves,  they  that of  reported  the  v.  estimates  d i f f e r e n t from  estimates  evaluates  stock  in which  r e s u l t s produced  for  consumer  demographic  i n s e n s i t i v e to of  the  rent  the  sets  (5.21) a  In  of  particular,  v as  zero, in  l i k e l i h o o d value  high  as  l e t alone  table  III,  earlier  5.2, from  v was  is  but  none  unity.  fixed  at  1 10  unity,  with  no  significant  reduction  i n the model's  explanatory  power.  4.  Red  House—Blue  Chapter for  correlation  (m=o,r). the  three  The  i s very The  zero,  maximum  were  These between  insensitive  results  the  household  two  tenure  demographic  of  insensitive  suggest  moving  that  options  choice.  estimate 0.66  therefore III.  This  played  f o r the  to changes  in table  also  role  terms  likelihood  t-statistic  reported  parameters  the  error  p a r a m e t e r s were  as  (a)  describes  between  corresponding  value  House  any have may  a,  two  of  a  moving  the  i n the value  re-estimated of  which  allows  options  i s 0.5004,  suggests  Estimates to  by  likelihood of  with  the  but  a. a  fixed  at  remaining  a. perceived little  or  underline  v a r i a b l e s - - b y d e f a u l t , they  similarities no the  assume  a  bearing  on  importance of major  role.  111  E.  Is  1.  Tenure  the  Full  Choice  Having considers demand  and  which  should  with  be  urged  of  which  the  i s done  model  L  equation model full are It  replacing  =  [ L  L  5.2 5.4  and  choice, explore  which  are  which and  jointly  the  whether  likewise.  In  conditional other  particular,  easier  to  are  estimate  estimates?  itself  i s to  into  but the  likelihood  *log  use  a  which  tenure  does  not  likelihood maximand  choice also  calculation.  in  5.1  with  an  5.3  are  i n c o r p o r a t e s the  marginal  share In  of the  maintained  set  of  results  two  that  earlier;  Consequently,  parameters  from  tables  are  i s the  quite  the  5.6  which  "logit  and  this appear  only"  devoted  logit  j3  to  i s twice  5.2.  similar  estimated  expenditures model,  described  VI.  compare  f o r the  as  same  in table  and  (5.22)  model.  summarized  difference,  Lt  the  Estimation  estimates  ] =  from  model.  to  P j  i s dropped  striking  services.  the  d j  j  is interesting  parameter  parameter  model  version:  Equations  the  model  equations  h  in  do  suggests  share  by  log  logit  to  a  transactions disutilities,  abbreviated  only  to  this  similar  method  tenure  i t is useful  cases  yield  incorporate This  estimated  transactions costs,  special  model  Alone  for housing,  One  Necessary?  c o n s t r u c t e d and  researchers there  Model  The  except  value  for  accommodation the  size  of i t s  for /3,  one the  1 12  counterpart asymptotic These  i n the  t-statistic  differing  active  role  disutility  To  (equation  resulting  log  favorably  to  using  full  the  rejected degrees  on of  This improved  the  the  for  full  1 5  the  tenure  contrast  the  10.49).  in light  choice  K,  i n the  parameters  full  and  of  the  the  the t r a n s a c t i o n s conditional  model  in table  parameters,  function  of  -70.2647  does  value  of  -47.6583  which  specifically,  the  likelihood  VI  demand  are  they  in equation  value  More  b a s i s of  suggests ability  that  to  demand  share  tenure  determing  the  full the  model joint  d e c i s i o n s over  marginal  of  the  explain  is particularly  in  surprising,  appear  likelihood  contrast  the  versus  yet  the  ratio  not  5.1.  The  compare  was  attained  logit test  were  model  with  is  five  freedom.  conditional  after  not  the  maximum  model.  the  In  logit  likelihood the  too  (1.72  .19084),  5.4b).  proxies by  not  in both  does  whether  evaluated  are  smaller  decisions.  parameter,  acceptable  (.38895 v e r s u s  i s much  j3 p l a y s  demand  test  model  results  which  conditional  function  full  clear  expenditure decision  tenure  the  going  to  that  housing  the  a  significantly  choice  solitary  regarding  i s made  q u a n t i t y of  provides  and  logit  model.  estimate  housing. /3 c o m e s  consumed.  It into 1 6  of  /3,  The the  i s only active  play  1 13  TABLE  VI  Maximum L i k e l i h o o d P a r a m e t e r Estimates f o r L o g i t Model Only 1  Parameter  0 8  Estimated Value  Asymptotic t-stat  .38895  1.72  2.6094  3.55  -2.4827  -3.49  -1.4843  -2.66  0.5577  2.63  k 5 kl 5 kw 8 kn  log  L  2  -70.2647  1. The f o l l o w i n g p a r a m e t e r v a l u e s were h e l d e s t i m a t i o n ; v = 1.0, 7 = 0, 7 = -1000, a = a c detaiIs.  fixed during this 0. See t e x t f o r  2. T h i s i s the value of the f u l l l i k e l i h o o d f u n c t i o n e v a l u a t e d at the parameter values which maximized the l o g i t likelihood function.  1 14  2.  Conditional An  analogous  subsection In  this  event  f m  Equations  procedure  i s t o drop  log  where  Share  t o that  the tenure  the likelihood  L = I I d *log h m m  i s as d e s c r i b e d  estimation  Alone  o f t h e share  described i n the preceding  choice  maximand  f  term  from  equation  becomes  (e ) = L d m m  i n 5.4.  This  equations  5.1.  (5.23)  strategy  u s i n g maximum  i s equivalent to  likelihood  e s t imat i o n . An not  immediate  offer  share  full  3.  equation. cannot  Concluding  be r e t r i e v e d  estimates  and  satisfy  but  demographic that  these  utility  i s that  transactions they  the share  i t does disutility  do n o t appear  therefore that  from  estimates  equations  upon  described i n this  I I I ) which  the precepts variables  the level  conditional of  (table  traditional  determine  alternative  in  of the  alone.  Remarks  parameter  that  It i s clear  estimation procedure  which  this  ( 6 , 5 ,6 , and 5 ), because k k l kw kn  model  The  with  a means o f e s t i m a t i n g t h e f o u r  parameters  the  problem  decisions maximizing  viable  variables  choice.  sense.  (price  services  The r e s u l t s  c a n be m o d e l l e d framework.  are statistically  the tenure  of accommodation  tenure  yields  o f common  dominate  economic  chapter  within  Moreover,  They  suggest  choice and  decision,  expenditure)  consumed confirm  a mutually the f u l l  that  both  consistent  model i s  1 15  preferable choice  or  to  one  which  conditional  limits  demand  itself  decisions  to  either  alone.  the  tenure  1 16  NOTES  TO  CHAPTER  FIVE  1.  I n t h e i n t e r e s t s o f l e g i b i l i t y , t h e 'h' s u p e r s c r i p t s h a v e been s u p p r e s s e d from t h e r i g h t hand s i d e of e q u a t i o n s 5.2 t h r o u g h 5.4. They a r e u n d e r s t o o d t o b e l o n g w i t h a l l p r i c e , expenditure, and q u a n t i t y terms.  2.  As d e s c r i b e d i n V a e s s e n (1984, p. 142), FLETCH i s a v a r i a t i o n of the V a r i a b l e M e t r i c Method, which i s a "robust implementation of t h c l a s s i c a l quasi-Newton approach."  3.  The b a s i c i n p u t t o t h i s XDFUNC(X,N) w h i c h g i v e s f u n c t i o n f o r any v e c t o r f u n c t i o n ' s domain.  4.  The a n a l y t i c d e r i v a t i v e s f o r L a r e q u i t e l e n g t h y , due t o the n e s t l e d l o g r i t h m i c and e x p o n e n t i a l f u n c t i o n s . Using numeric d e r i v a t i v e s t h e r e f o r e saves a great deal of time and r e d u c e s t h e danger o f programming e r r o r s .  5.  Other procedures f o r i n c o r p o r a t i n g demographic v a r i a b l e s r e v i e w e d by P o l l a k a n d W a l e s (1981) i n c l u d e t h e Gorman o r r e v e r s e Gorman s p e c i f i c a t i o n s ( w h i c h a r e c o m p o s i t e s o f t h e s c a l i n g and t r a n s l a t i n g procedures) and the m o d i f i e d P r a i s H o u t h a k k e r s p e c i f i c a t i o n ( w h i c h may y i e l d a t h e o r e t i c a l l y p l a u s i b l e demand s y s t e m o n l y i f t h e o r i g i n a l system c o r r e s p o n d s t o an a d d i t i v e d i r e c t u t i l i t y f u n c t i o n ) .  6.  Demographic t r a n s l a t i n g accomodation s e r v i c e s .  7.  In our model, demographic s c a l i n g and demographic translating yield equivalent preference orderings i f f m  7  i 8.  +  =  i  7  i  d  r o u t i n e i s a f o r t r a n program the value of the l o g - l i k e l i h o o d X(N) o f parameter v a l u e s i n t h e  parameters  are introduced  only f o r  * i  F o r e x a m p l e , /3 o f t e n s t a l l e d a t v a l u e s o f .03 o r l e s s , suggesting that less than 3 percent of household expenditure i n c r e a s e s go t o w a r d s a c c o m o d a t i o n s e r v i c e s . The l i k e l i h o o d v a l u e s a t t h e s e s t a l l e d e s t i m a t e s were n o t at a l l c o m p e t i t i v e with those r e p o r t e d l a t e r i n t h i s chapter.  11 7  9.  The g r a d i e n t s o f t h e l i k e l i h o o d f u n c t i o n w i t h r e s p e c t t h e 7* w e r e n o n z e r o . T h i s s u g g e s t s t h a t t h e LES s p e c i f i c a t i o n may be s o m e w h a t restrictive.  10.  Further d e t a i l s in appendix E.  11.  T h e u n i t s f o r K, a n d h e n c e f o r t h e 6 i n t a b l e 'utils'. But as d i s c u s s e d l a t e r i n the t e x t , m e a n i n g f u l l y p r e s e n t e d i n terms of the impact on t e n u r e c h o i c e probabilities.  12.  The v a l u e s o f [ l - e x p ( - / < ) 3 r e p o r t e d i n t a b l e IV a r e almost u n i t y i n some c a s e s , s u g g e s t i n g t h a t h o u s e h o l d s w o u l d rather forego almost t h e i r e n t i r e income i n o r d e r t o a v o i d a move. While t h i s i s h i g h l y dubious, i t b r i n g s t o mind the survey r e s u l t s of the R o s k i l l study (1970), where e i g h t p e r c e n t o f t h e s a m p l e s t a t e d t h a t " n o sum o f m o n e y " c o u l d c o m p e n s a t e t h e m f o r h a v i n g t o move ( r e p o r t e d i n D y n a r s k i (1986)).  13.  R e c a l l t h a t t h i s sample r e l o c a t e d from one c i t y  14.  As Kent (1983) p o i n t s o u t , " t h e r e i s n o t one income e l a s t i c i t y o r one p r i c e e l a s t i c i t y o f h o u s i n g demand. Rather, there i s a s e r i e s of e l a s t i c i t i e s . " These c o r r e s p o n d t o t h e v a r i o u s stages of d e c i s i o n making i n t h e housing p r o c e s s , such as tenure c h o i c e and c o n d i t i o n a l demand. B e c a u s e d i f f e r e n t s t u d i e s f o c u s on d i f f e r i n g combinations of these housing d e c i s i o n s , t h e i r r e s u l t s are not d i r e c t l y comparable.  15.  These models a r e n e s t e d i n t h e sense t h a t (a) they have t h e same d e p e n d e n t v a r i a b l e s , a n d ( b ) o n e i s e s t i m a t e d freely while the other i s evaluated with a l l parameter values restricted to the logit-only values reported in table VI.  16.  A n a d d i t i o n a l t e s t was p e r f o r m e d t o d e t e r m i n e w h e t h e r t h e v a l u e o f o f j3 e n t e r i n g t h e c o n d i t i o n a l h o u s i n g demand e q u a t i o n d i f f e r e d from t h a t e n t e r i n g t h e t e n u r e choice equations. T h e r e was n o s i g n i f i c a n t d i f f e r e n c e . This result provided confirmation of the consistency hypothesis; n a m e l y , t h a t t h e same s e t o f p r e f e r e n c e s u n d e r l i e b o t h aspects of the household's housing choice. This contrasts favorably with r e s u l t s reported i n King (1980).  on  these  exploratory  crosstabs  excludes households to another.  are  to  provided  III are K i s more which i t has  who  may  have  1 18  VI. A.  E v a l u a t i n g Tax Mortgage As  been  Interest  discussed  developed  policies rate  of  as  housing  which for  each  tax  taxable  deductions the  will  of  which  1  mortgage  income.  are  an  this  change  model  impact  on  determine  has  taxation  i n the  preference  will  effective  prices  or  parameter the  extent  into  welfare  gains  i s evaluated  in this  chapter  United  States  expenses  housing to  declare  from  This  or  to  losses  a  comprehensive  = 1  of  the  from  and  income  yet  income  taxes  systems  interest  income,  landlord  tax  the  these  Homeowners  mortgage  gross  property  i n Canada,  Britain.  deduct  imputed  subsidy  comprehensive  (imputed  T  allowable  Great to  payments  is  are  which  in  in those  payments not they  themselves.  implicit  of  the  not part  and  other  required  interest  integral  and  a  five  While  allowed  income  The  translated  countries are  precept  A  typically  household.  two  receive  Deductibility  evaluating alternative  housing.  in chapter  reform  deductibility  both  to  to  are  Tax  introductory chapter,  taxation  changes  Example  Property  view  f o r each  An  household.  The  from  a  relate  estimated these  and  i n the  with  they  expenditures values  Reforms;  tN  or  tax,  t(G-C)  owner-occupiers  income  otherwise)  income  =  to  a  tax  should  which be  violates states  taxed  l a n d l o r d ' s tax  the  that a l l  similarly. i s given  by  (6.1)  Under  1 19  where N  -- n e t r e n t  G  -- g r o s s  C  -- u s e r  t  -- l a n d l o r d ' s m a r g i n a l  Compare  this  rent cost  of c a p i t a l  to the housing  plus tax  operating  rate  related  expenditures  2  income  taxes  T  paid  by t h e  h homeowner allowed  who  does  t o deduct  not d e c l a r e gross a portion,  rent, but i s nonetheless  s, o f h i s u s e r  costs  from  other  income;  T  =  (6.2)  -t(sC)  h  In  a competitive  differentials both  cases,  costs:  market  will  gross  f o r housing  be t r a n s l a t e d rents will  be  accommodation,  into just  differences large  enough  these  tax  in rent.  to cover a l l  3  G  =  (6.3a)  C  1 G  =  (6.3b)  Cd-ts)  h  Thus,  t h e s u b s i d i z e d homeowner  services  at the reduced  rate  of  r e c e i v e s $1 $(1-ts).  worth  In  of  housing  120  In  the  United  state  and  local  value  for  s  s=0.682  taxes  figures.  approach  in computing reform  implicit  preceding price  The quite  different  from  However, announced  on  deductions  the  were  that  to  to  a  certain  reform  of  the  owner  United  so  uses  uses  interest  similar  by  i s the  removal  setting  s=0  effective  we  1978  this  that the  5  political  begin  in  of the  rental  was  specifically,  the  reform  or  in  taxes  with  would  not  of  United  are  party  introduce  power  in  the  implemented" that  i n Canada economic  evaluated  the  is  s=0.  i t is clear  appeal  grounds  housing  Conservative  governing  and  the  local  they  policy  debate,  occupied States  nor  Progressive  on  here  such next i t  was  the  despite i t s  theory.  6  is  h )  o the  a  authors  i n c r e a s i n g the  become  While  h  where  these  payments  21,  considerable  (p  takes  implemented  income,  federal  shortcomings  More  is  in  mortgage  they  subject  has  by  treatment  September  election.  obvious  tax  taxable  federal  proposal  This thereby  from  Neither  deductible  (1980)  (1969)  (1979)  mortgage  the  owner-occupiers.  Canadian  Kingdom.  Laidler  Rosen  Kingdom  income,  and  s.  subsidy.  by  King  evaluated  equations,  faced  United  and  payments  taxable  large.  purposes,  the  interest  from  is quite  d e d u c t i b l e , and  tax  mortgage  deductible  6.2  In  are  the  where  estimation  payments  The  are  in equation  for his  comparable  States,  =  (p  2  subscripts  states,  ) o  *  (1-ts)  1 '1'  and  respectively.  '2'  denote  Here,  s  the  i s the  pre-reform  and  explicit  price  postof  121  owner  occupied  occupied  housing  price,  p  .  expressed  That  as  a  share  of  the  total  owner-  i s ,  o s  =  (w+5+(l-u)r  )/p m  and,  as  described  in chapter  w  —  true mill  6  —  rate  —  mortgage  r  o  rate  4,  for local  property  taxes  of d e p r e c i a t i o n interest  rate  m 1-i>  —  Household e  =e 1  share  dwelling  expenditures  unit  value  are  not  affected  particular  tax  reform  by  subject this  to  mortgage.  reform;  thus,  =e. 2 Using  chapter  this  thus  application Secondly, research some  of  of  s e v e r a l advantages.  the  housing  i t allows and  light  housing  has  on  related a  policy.  for  demand  f o r more work  recurring  by  earlier  issue  First,  model  direct  the  example i t is a  developed  in  this  direct  earlier.  c o m p a r a b i l i t y between authors.  i n the  context  Finally, of  i t  Canadian  this sheds  1 22  B.  Ef f i c iency  1.  Equivalent One  Gain  of  a  of  the  most  criticizing  the  implicit  that  of  which  its  to  cost The  by  A  subsidy  serious  to  is  derive  grounds  owner-occupiers  inefficient from  i t do  for has  because  not  fully  been the reflect  government.  efficiency  first  and  subsidy  households  the  Reform  persistent  efficiency.  benefits  Tax  aspects  calculating  the  of  this  tax  reform  associated equivalent  may  be  gain  evaluated  (EG  ) for h  each  household.  additional in  the  as  well  This  income  which,  pre-reform off  as  is defined  state  (following King(1981))  i f i t were  disposed  of  by  the  has  utility  (v  7  fully  ) for  any  household  ,e ) , w o u l d make t h e h o u s e h o l d just 1 1 i n t h e p o s t r e f o r m s t a t e ( p ,e ) . Once the  i t is  been  the  (p  2 reform  as  specified, household  the  post-reform  2 level  of  is readily calculated:  2  v  = V(p 2  ,e)  = max  [V  2  More  (p  ,e),V  0 2  f o r m a l l y , EG  (p  ,e),V  r 2  is defined  (p  ,e)]  (6.4)  s 2  implicitly  for each  household  by V(p  ,e 1  There  are  three  distinguished; which  may  apply  measures these to  +EG)  =  of  left  (6.5) 2  equivalent  correspond  the  v  1  hand  to  the  side  gain three (LHS)  which  need  tenure of  to  be  choices  equation  6.5.  1 23  Thus,  we  have  V  ( p ,e+EG ) = v 1 o 2  (6.6a)  o  ( p ,e+EG ) = v 1 r 2  (6.6b)  r  ( p ,e+EG ) = v 1 s 2  (6.6c)  s  V  V  These  c a n be s o l v e d  model  described  explicitly  as f o l l o w s ,  based  on t h e L E S  earlier:  0 EG  = exp[v o  + *c(d)-b(0) ] * ( p 2  )  -  ( e - p y -y ) o a c  (6.7a)  -  ( e - p y -y ) r a c  (6.7b)  o  0 EG  = exp[v r  EG  2  true  among EG  This  point  )  K  r  = - ( e - p x -y ) + s s s c  The value  + (d)-b(0)]*(p  measure  these. = min  -0 1/(1-0) [ ( x -7 ) exp(v )] s a 2  of equivalent  gain  That i s , [ E G ,EG ,EG ] o r s  is illustrated  in figure  10.  i s given  (6.7c)  by t h e m i n i m u n  124  Figure  10  Choosing the C o r r e c t Measure of E q u i v a l e n t  Gain  1 25  It  graphs  V j  ( p ,e+EG) 1  f o r j=o,r,s.  In t h i s  example,  EG=EG o  because  v  = V 2  o  ( p ,e+EG ) 1 o = max[V j = V(p  ( p ,e+EG )|j=o,r,s] 1 o  ,e+EG 1  This into  means  that  owner-occupied  equal  to v  accommodation,  i n the state  ( p ,e+EG  household the EG  1  shown  in figure  chooses  pre-reform from  before  zero EG  8  i n figure EG .  o  into  In t h i s 10 l e a d s  could,  by c h o o s i n g  realize  a level  of  t o move utility  ). o  10, t h i s  t o move  state.  reaches  (6.8)  the household  2 As  ) o  need  not imply  owner-occupied example, to a  that the  accommodation  increasing  tenure  the value  switching  in of  decision  1 26  2.  Deadweight As  noted  that  the  cost  to  of  the  where  Loss  of  a  Price  earlier,  a  tax  benefits derived the  government.  deadweight  TL  This  loss  of  a  DL  = TL  reform.  Estimating  this  (or  loss  been  interest The  a  do  not the  fully  to  reflect  following  extent its  definition  EG  (6.9)  foregone  point  some in  tax  revenues  related)  due  measure  the  debate  about  i s most  easily  outlined  to  of  the  efficiency  mortgage  standard to  pure  argument  figure  11.  rental price  In  the  of  p  pre-subsidy and  with  state,  consume  an  homeowners  amount  1 A  the  deductibility.  reference face  inefficient  prompts  -  or  focal  is  reform  loss  a  reform  therefrom  tax  has  i s the  Subsidy  subsidy  lowers  the  cost  to  to  consume  a  . 1  p  =  p  2 homeowners  x  (1-ts)  and  encourages  1  greater  amount,  x  .  The  annual  cost  to  2 the  government  ACDF,  while  household given  by This  are  no  their the  of  the  this  increase  i s given BCD,  by  standard  housing of  changing  The  by  consumer  deadweight  loss  the  rectangle  surplus is  for  the  therefore  triangle.  argument  stock  is represented  in marshallian  ABDF.  Harberger's  transactions  face  program  applies  to  disutilities  and  effortlessly  from  prices  and  a  world  i n which one  incomes.  in  which  households  period  to  the  there adjust next  in  Deadweight Loss of a P r i c e Subsidy  '  >  128  In  our model,  follows. given  The t a x l o s s  d =1 2  reform  of  argument  resulting  from  c a n b e made  the i m p l i c i t  as  subsidy  i s  by TL  where  the analogous  = d * ( p - p )*x ( p ,e) 2 1 2 2 2 i f the household  s t a t e , d =0 2  efficiency  gain  (6.10)  i s an o w n e r - o c c u p i e r  otherwise.  I t remains  9  (EG ) w h i c h  corresponds  i n the post-  to specify  most  t h e measure  closely  to that  m implied  by t h e s t a n d a r d  relocate  each  indirect  utility  implicitly  1  where  (t=1,2).  form  defines  V(p  For  period  model,  This  f o r both  equivalent  households i s derived  sides  a r e assumed t o by u s i n g  of the equation  which  gain:  ,e+EG) = V ( p ,e) 2  t h e LES s p e c i f i c a t i o n ,  the  this  (6.11)  c a n be  readily  solved  f o r EG  : m  /3 EG  =  (p /p 1 2  m  The  is  deadweight  therefore  DL  =  )  ( e - p 7 -7 ) 2 a c  loss  given  ( e - p 7 -7 ) 1 a c  (DL ) f o r a homeowner m  in a  (6.12)  "move-move"  world  by  ( p - p ) [ ( 1 - / 3 ) 7 +/3(e-7 ) / p ] 1 2 a c 2  m  -  (p /p 1 2  /3 )  ( e - p 7 -7 ) + 2 a c  ( e - p 7 -7 ) 1 a c  (6.13)  129  It  is clear  that  the  deadweight  loss  is  zero  for  p  =p 2  (that  i s , when  that and  the  there  expression  increasing  as  is  no  for  the  subsidy).  deadweight  level  of  And loss  subsidy  appendix is  (p  exception  to  effect",  represented  this  rule  here  by  of  the  thumb  -p  )  is  positive  increased.  A  2  arises  expression  when  (p  /p 1  too  shows  generally  1 possible  F  1  )  the  ,  "income  becomes  2  large. It  is  instructive  expression  for  to  contrast  this  result  loss  )  a  deadweight  (DL  in  with  the  "stay-stay"  world.  s This of  is  obtained  equation  by  6.11,  using  the  yielding  direct  EG  =  utility  xcnet  -  form  xcnet  2  on  both  sides  . 1  Thus, DL  =  (p  =  (p  =  since  x  (p  =  0  =  (x  -p 1 2  )  of  deadweight  xcnet  +  xcnet  2 -  [e-p 2  )x  +p 2  =  (x 2  (x  2  result  subsidy  quantity  2  -p )x 1 2 2  s  This  )x  1  ) s  ] +  ) -y 2 c  (x s -  p  2  (x 1  [e-p  (x  ) -7 ] 1 s 1 c  ) s  1 (6.14)  2  price  -p 1 2  ) s  is  not  when  surprising.  i s equivalent  housing loss  with  services a  households  fail  to  relocate.  1  lump  to  states  lump  sum  consumed  is  sum  a  It  transfer.  that  transfer fixed;  and  a  housing  when  the  there  is  no  130  It  is clear  implicitly  assumes  overestimate section  3.  the  model  the  of  simulate  impact  on  tenure  with  transactions result  of  results Not leads  a  relocate tenure  doubles  possible  is  price  subsidy.  in this  The  next  regard.  and  tax  in previous  reform  deadweight  model  and  1 0  household  and  loss. once  utilities  to  estimate  This  i s done  with are  chapters  the  reduced  relocation.  The  contrasting sets  i n t a b l e s VII  and  VIII.  the  simulation with  larger  period.  number  i n marked  the  price  the  post-reform  subsidy  accept  This VIII,  will systematically  developed  proposed  number  And  1 1  i s much m o r e  the  a  which  of  the  of  the  effect  apparent.  of  the  mover/owners  to  94,  model  which  price  Introducing out  a  of  standard  households  as  subsidy  the of  subsidy a  137.  This  happily  where  substantially  choice  demand  standard  compared  in either  of  model,  Efficiency  the  surprisingly,  to  nearly  the  model,  loss  choice  residential  are  on  housing  to  once  standard  empirical evidence  us  twice;  the  'move-move' w o r l d ,  Empirical Evidence  enables  on  a  deadweight  examines  The  its  therefore that  a  period. the  Most  windfall  r e p o r t s the loss  of  the  to  negligible  c o n t r a s t between  which  deadweight  has  contrast  the  price  t r a n s a c t i o n s model,  e f f e c t ' on  households  gain  mean  the  which  two  tax  subsidy  remain  befalls  models  loss,  tenure  choice  where in  stationary,  but  them.  reappears  equivalent  in  gain,  for owner-occupied  table and housing.  131  T A B L E  Effect  of P r i c e  V I I  Subsidy  on  Standard Model  Tenure  Choice  Transactions Model  # of pre-reform mover/owners  50  5  # of post-reform mover/owners  94  6  # of pre-reform stayers  79  129  # of post-reform stayers  39  130  # of pre-reform mover/renters # of post-reform mover/renters  sample  size:  137  1 32  TABLE  VIII  D e a d w e i g h t L o s s Due t o P r i c e Subsidy ( i n c o n s t a n t 1979 d o l l a r s )  Standard Model u  mean  tax loss  mean  equivalent  mean  deadweight  size:  137  ~T$T  2973  675  gain  1716  615  loss  1257  60  deadweight l o s s as a percentage of tax l o s s  sample  r  Transactions Model  42.3%  8.9%  133  It  shows  .($2973  that  t h e mean  versus  $675) where  disutilities. occupiers part by  This  who  now  t o t h e new  the  accommodation as  equivalent Indeed,  the  a r e no  in part  to  subsidy  occupiers,  those  a  each  i s much  higher  transactions original  subsidized in place.  And  o f whom h a s  relatively  owner i t i s due  been  large quantity  in  induced of  services. i s consistent with  over  earlier  be  t o consume  gain  deadweight  must  from  there  i s due  owner  subsidy  And,  tax loss  falls  forty  loss.  deductibility  considerably  percent This  authors,  1 2  the  of  the  figure  and  i s an  continues  standard short  of  subsidy  argument, the tax  yields  t o be  such  o f why  loss.  nothing  i s comparable to the indication  t h e mean  findings  mortgage  a controversial  but  tax  of  interest reform  proposal. In nearly the  the t r a n s a c t i o n s model, matches  subsidy  sense,  Thus  captures  previous  following  conclusions  as mortgage  to  8.9  percent In  one.  very of  this  1 3  incorporate  models  regarding  interest  gain  loss.  efficient  into  has  the  resulted  in  inefficiency  deductibility  of  for  housing. the truth  presented  only  reasonably  disutilities alarming  Only  deadweight  failure  owner-occupied  models  into  equivalent  loss.  that  s u b s i d i e s such  However,  is a  tax  appear  unjustifiably  two  translates  reform  i t would  transactions  price  the corresponding  outlay  the tax  t h e mean  is likely  here.  the period  the reform.  The  t o l i e somewhere  reason  immediately  Over  time,  i s that  between  the  the simulation  preceeding  the cumulative  and  immediately  number  of  134  households household  who  relocate  does  consumption  move,  decision  will  slowly  i t i s likely  increase.  t o be  by t h e f a v o r a b l e  A n d when a n y  influenced  price  of  in  i t s  owner-occupied  housing. The  result  increase  of this  i n the annual  subsidy.  So w h a t  occupiers  i n the short  loss,  process  deadweight  i s in effect term  due t o t h e s u b s i d y ' s The  profile  pace  actual  of this  not modelled  ongoing  under  here,  sum g r a n t  t o owner-  into  and open-ended  depends  upon  may  nature.  the demographic  consideration,  which  deadweight  govern  as w e l l  as  the timing  other of the  moves.  Distributional Evaluation  1.  Equivalent  The  however,  Expenditure  preceding  representation  analysis  of household  further  required.  measurable  and f u l l y  Donaldson,  a n d Weymark complete  only  utilities.  In p a r t i c u l a r ,  expenditures,  have  requires  restrictions  equivalent  numbers  cumulative  attributable to the  s t e a d i l y evolves  C.  are  loss  a lump  evolution  of the population  influences  i s a parallel  an o r d i n a l  For our purposes,  on t h e h o u s e h o l d we  assume  as defined  comparable, (1984). numerical  that  below,  functions  household  are translation-scale  as defined This  utility  assumes  by  Blackorby,  that  a l l  utility  s i g n i f i c a n c e , and allows f o r  135  explicit  comparisons  The  utility  between  measures  households.  are normalized  expenditure  metric. "  expenditure  f o r the t ' t hstate  1  In p a r t i c u l a r ,  through  we  define  (E ) as t h a t  a money o r  the  sum  equivalent  o f money  which,  t if  spent  (p*),  by t h e h o u s e h o l d  would  household  yield  t King is  t.  reference  level  of u t i l i t y  enjoyed  price by  vector  that  That i s ,  ) = V ( p ,e ) = v t t t  (1981)  the average  t o some  t h e same  in state  V(p*,E  subject  suggests  that  s e t of p r i c e s  (6.15)  a natural  prevailing  reference  price  i n the pre  vector  reform  period. The  value  v  denotes  a particular  i n d i f f e r e n c e curve;  that  t which  corresponds  attain  the  subject  t o t h e maximum  to the state  minimum c o s t  utility  vector  of a t t a i n i n g v  the household can  ( p ,e ) . t t  subject  And E  i s simply t  to the  reference  t prices,  p*.  This  concept  of equivalent  to  t h e measure  of equivalent  In  particular,  i f the pre-reform  prices  we  have  expenditure  gain  used  i s closely  i n the previous  p r i c e s a r e used  as  related section.  reference  V(p*,E 2 —>  V ( p ,E ) = v 1 2 2  —>  E 2  And,  ) = V ( p ,e ) 2 2  of course,  = e +EG 1 E  =e  when  p*=p  1 1 As  was  equivalent three For  1  the case  with  expenditure  tenures  which  .  equivalent gain,  three  measures of  c a n be d e r i v e d , c o r r e s p o n d i n g  may  apply  t h e LES s p e c i f i c a t i o n  used  t o the l e f t here  we  hand  side  to the o f 6.15.  have:  0 (E  ) = exp[v + ( d ) - b ( 0 ) ] o t t  ( p *) o  (E  ) = exp[v +/c(d)-b(0)] r t t  ( p *) r  (E  ) s t  K  +  (p * ) 7 + 7 o a c  (6.16a)  +  ( p *>7 + 7 r a c  (6.16b)  0  and  =  then,  [exp(v  -0 1 / ( 1 - 0 ) )*(x -7 ) ] + t s c  analogously  E  = min t  to the earlier  [(E ) ,(E ) ,(E ) ] o t r t s t  (p * ) x + 7 s s c  (6.16c)  derivation:  (6.17)  1 37  2.  Social  Welfare  Having measurable to  selected index  measuring  flexible  and  Proportional Social  a  fully  of household  aggregate  social  welfare  t  utility,  welfare.  h  This  and we  translation-scale  now  turn  research  function developed  W (E ) = Z [ (E ) t  comparable  Gain  - (t-D*TL/H]  our  attention  an  ethically  uses  by A t k i n s o n  (1-e)  (1970):  /(1-e)  t h e  not=1 (6.18)  W t  (E ) = Z l n [ ( E ) - (t-l)*TL/H] t h t h  e=1 where  the expression  equivalent equal  gain  value  each  period  household's  ( t = 2 ) by  of the tax l o s s  an  resulting  amount from  the  1 5  The welfare  reduces  i n the post-reform  to the average  reform.  (t-1)*TL/H  parameter  e measures the c u r v a t u r e  indifference  loci.  Three  values  of  are of  the  social  particular  interest:  A  e=0  a  e=1  a proportional utilitarian  e=»  a Rawlsian  useful  distributional social  gain  simple  summary effect  utilitarian  welfare  statistic  measure  measure  f o r e v a l u a t i n g the  of the tax reform  (a) d e f i n e d  measure  implicitly  by  i s the proportional  138  W  That  i s , a gives  initial yield reform  the  equivalent  the  (oE 1 1  ) = W  proportion  by  income  reference  to  This the  ) 2  same a g g r e g a t e  state.  (E 2  can  would level  be  Atkinson  (6.19)  which  need of  each  to  be  welfare  solved  increased found  explicitly  measure  household's  described  in  for  a  in order  the  to  post  with  above:  1/d-e) a  =  [W  /W 2  ]  e  not=1  1 (6.20)  a  =  exp[(W  -W 2  where  H  i s the  number  of  one  i n d i c a t e s the  welfare  has  been  3.  for  Table social from  gives  welfare  the  tax  presented The again  Evidence  IX  for most  between  relocation  and  both  as  on  the  for the  of  amount  by  which  aggregate the  a  social  reform,  after  of  Welfare  pre-reform  proportional  various  result  shows  values and  from  models.  disutilities  which  result  Aggregate  standard  striking two  a  to  The  taxes.  estimates of  reform  the  degree  increased  increased  Empirical  e=1  households.  exceeds  adjusting  )/H] 1  The a  and  social  gain  of  These  the  e.  resulting results  transactions  table  IX  standard  strong  post-reform  models.  i s the  contrast  model  without  aversion  to  are  the  price  once  139  TABLE Effect  of Price  Subsisy  STANDARD  (e)  Pre-reform value of SW index [W ( e ) ] 1  IX on  Social  Welfare  MODEL  Post-reform value of SW index [W ( e ) ] 2  Proportional social gain of reform [o(e)]  0.0  2.743*E+6  2.53l*E+6  0.9227  0.1  1.121*E+6  1.038*E+6  0.9176  0.5  3.769*E+4  3.564*E+4  0.8939  1 .0  1.341*E+3  1.319*E+3  0.8536  1 .5  - 2 . 128  -2.383  0.7977  2.0  -8.9l*E-3  -1.23*E-2  0.7268  TRANSACTIONS  MODEL  0.0  2.700*E+6  2.696*E+6  0.9985  0.1  1.l05*E+6  1.l02*E+6  0.9975  0.5  3.734*E+4  3.722*E+4  0.9936  1.0  1.337*E+3  1.336*E+3  0.9886  1.5  -2.168  -2.185  0.9847  2.0  -9.44*E-3  -9.59*E-3  0.9846  1 40  subsidy (e=0)  modelled  one  here.  could  reduce  expenditure  by  7.7  as  be  i f the  i t would  even  stronger  inequality In  as  undisturbed version, subsidy  the  the  net  social  price  effect  Even  strong  transactions  model  corresponding These to  the  significant  model.  Any  tax  will  require  That  i s not  reform its  most  subsidy  that  in  e.  the  in the  assistance.  (or  we  that  may  best  standard  And  of  in  In  to  fact, as  results  are  a  greater  conclude  are  e x p l a i n s why  utilitarian  loss  overcome  0.15  percent. e=2.0),  just  in  the  this  standard disadvantage  take  those a'(e)  is placed  not  least 0.  vary  households  advantage  <  the on  model.  does  those  who  impacts.  discussed,  standard  that  a  attributable  emphasis  loss  to  the  model.  distributional as  the  each  (at  standard  in the  to  largely  i s in contrast  heavier  able)  by  aversion  deadweight  model  off  on  reducing  deadweight  hopes  is  l a r g e measure  favourable  of  well  introducing  expenditure  This  are  poorly  as  The  simple of  by  for the  consequences  Thus,  inclined  obtained  a=72.7  level  society  the  welfare  a=98.5.  here.  version  equivalent  function takes  inequality  which  much m o r e  leave  For  social  presence  case  distributional  changes are  the  pre-reform  t r a n s a c t i o n s model  results  reform  utilitarian  introduced.  equivalent  of  simple  increases).  that  particularly  rates  Note  on  shows  divergent  were  e  built-in  figure  still  subsidy.  to  pre-reform  the  welfare  ( i e , as  household's a  and  reform  is equivalent  with  with  household's  c o n t r a s t , the  by  the  each  percent  aversion  sharp  Even  of  the  require  with who  141  The  t r a n s a c t i o n s model  distributional somewhat price lump  consequences  surprising.  subsidy sum  to  households.  And  than  1  would  have That  results  seriously  earlier.  As  unity  the  was  for  the And  serious half  the  between  case not loss  case the  who  the  basic  shown  selected for  subsidy  the  values  full  social  a  rate,  remains  X,  that  i n the their  are  reform's  much  measure large  that  a  like  better  such  a  off  reform  most  of  standard  the model  consumption  in  subsidized in place  impact  on  aggregate  do  not  welfare.  reappeared  when  the  model  a p p l i e d at  half  the  rate  the  values  of  a  are  a l l close  i n the  t r a n s a c t i o n s model,  of  e  the  welfare  standard  model  when  subsidy  although intact.  a  by a l l  was proposed  subsidy.  surprisingly, in  who  in table  priori  is  section,  very  and  the  implications.  reform  findings  similar  by  of  result  previous  in equal  are a  This  works  suggests  adjust  households  previous e and  by  households  a  i n the  speculate  the  introduced  test  homeowner  n e u t r a l view  subsidy.  financed  distributional  i s not  same  the  largely  t r a n s a c t i o n s model  might  aggrevate  These to  , one  a  discussed  because  Those  of  homeowners  negative  from  response.  used  6  this  inequality  As  i n the  grant  renters  takes  the  the  negative  shows  a  less  is applied  at  correspondence  to as  TABLE Comparative  X  E f f e c t s of Half  STANDARD  Proportional  versus  Full  Subsidy  MODEL  social  gain  [o(e)]  (e)  Half Subsidy  Full Subsidy  0.0  0.9600  0.9227  0.1  0.9580  0.9176  0.5  0.9488  0.8939  1.0  0.9345  0.8536  1.5  0.9160  0.7977  0.1  0.8934  0.7268  TRANSACTIONS  MODEL  0.0  1.0007  0.9985  0.1  1.0003  0.9975  0.5  0.9993  0.9936  1.0  0.9990  0.9886  1.5  1.0014  0.9847  0.1  1.0093  0.9846  1 43  D.  An  Assessment  There grounds the  appear  for  of  Price  to  be  introducing  results presented However,  the  Subsidies  efficiency  a  subsidy  price this  chapter  vehemenence  tax  households  respond  to  i t .  response  by  households;  deadweight  loss  unfavourable In little  move price the  ones  who  of  benefit  to  making  for  subsidies  on  and  this  to  order  great  by  move.  how  predicts a  a  a deal  of  distinctly  that  subsidy. take  advantage  likely  be  influence  housing  decision.  those by  of  the  who  the  They  do new  are  subsidy. welfare  slight  to  very  Few  However,  reasons  lead  to  predicts  in  r e s u l t i n g from  the  transactions  i t may  be  on  part  the  numerous  the  desirable of  to  existing  horizontal  inequities. The  perspective  applicable  in  the  households  will  of  short  relocate  of  that  of  housing.  social is  the  remortgaging  could  model  model  the  practical  due  view  None  such  opposes  consequently  their  from  impact  favour  i s compounded  in  will  owner-occupiers  However,  homeowners,  relocate  most  equity  effects.  owner-occupied  when  nor  homeowners.  one  one's  standard  r e s u l t of  reasons  would  upon  that  grounds  for  which  transactions  direct  to  aggregate  transfers  out  a  unrelated  The  rule  as  structure  model.  the  bother  price  for  The  distributional  happens  reduced  depend  a r i s e s , and  contrast,  households  may  with  particular  wholesale  Homeowners  neither  in  reform  for  the run. for  transactions Over  time,  model more  is and  l a r g e l y demographic  more more reasons.  As  144  they to  do  so, the cumulative  resemble The  this  more  proposed  housing  particularly  closely reform  demand  model  in light  impact  that  of the price  subsidy  p r e d i c t e d by t h e s t a n d a r d  i s t h e r e f o r e unambigously on b o t h  of i t slong  equity term  1 7  come  model.  rejected  and e f f i c i e n c y  effects.  will  by  grounds,  1 45  N O T E S TO  The t e r m " t a x r e f o r m may be  CHAPTER  reform" i s used a " g o o d " one o r  SIX  here i n a n e u t r a l a "bad" one.  The l a n d l o r d ' s m a r g i n a l t a x r a t e i s assumed c o n s t a n t over the r e l e v a n t range, and e q u a l t a x r a t e o f t h e homeowner.  sense.  A  h e r e t o be to the marginal  However, h o u s i n g m a r k e t s a r e not always c o m p e t i t i v e , and t h e n o n - t a x a t i o n o f n e t i m p u t e d r e n t a l i n c o m e becomes an i s s u e as w e l l . F o r e x a m p l e , t h e R o y a l C o m m i s s i o n on T a x a t i o n i n 1966 c o n c l u d e d t h a t t h e e x c l u s i o n o f imputed r e n t f r o m t a x a t i o n c o n s t i t u t e d "a s u b s t a n t i a l p r e f e r e n c e for homeownership".  so  The P r o g r e s s i v e C o n s e r v a t i v e s d i d i n f a c t win t h e n e x t e l e c t i o n , but d i d not r e t a i n o f f i c e l o n g enough t o implement t h e i r proposed reform. S e e , f o r e x a m p l e , "A H o t D e b a t e " M a i l , A p r i l 19, 1 9 7 9 , p.B2. A useful Shaffner In  this  review of (1979).  can V  be (p  o evaluated  seen  the  shortcomings  by  vector  Toronto  Globe  i s provided  noting  ,e+EG) = max  at  that  [V  1  (p j  the  intercept  (p  &  by  ,e) r e p r e s e n t s t h e r e l e v a n t t p r i c e v e c t o r and e x p e n d i t u r e l e v e l f o r p e r i o d t . The p r e r e f o r m s t a t e i s d e n o t e d by t = 1 , t h e p o s t - r e f o r m s t a t e by t=2. Where t h e r e i s a n e e d t o s p e c i f y t h e p r e c i s e t e n u r e i n q u e s t i o n , t h e t e x t uses (p ) , where j d e n o t e s t e n u r e . j t This  section,  these  i n the  ,e+EG)  |  j=o,r,s]  1 ( i e , when  EG=0).  146  9.  This d e f i n i t i o n of tax l o s s a p p l i e s model and t h e t r a n s a c t i o n s model.  to  both  the  standard  10.  The all  11.  N o t e t h a t some h o u s e h o l d s s t i l l c h o o s e n o t t o r e l o c a t e even when t h e r e a r e no t r a n s a c t i o n s d i s u t i l i t i e s i n t h e m o d e l . The r e a s o n i s t h a t t h e s e h o u s e h o l d s e n j o y a n o m o l o u s p r i c e advantages i n t h e i r present l o c a t i o n s .  12.  King (1981), f o r example, r e p o r t s t h a t the e q u i v a l e n t g a i n f o r o w n e r - o c c u p i e r s i n h i s sample i s j u s t o v e r fifty percent of the c a l c u l a t e d tax l o s s . While t h i s i s of s i m i l a r magnitude to the r e s u l t s reported here, a s t r i c t comparison i s of dubious v a l u e because King e v a l u a t e s h i s reform i n the c o n t e x t of a d i f f e r e n t h o u s i n g market with d i f f e r e n t p r o p o r t i o n s of owners v e r s u s r e n t e r s .  13.  However, a n o t h e r p o s s i b l e s o u r c e of i n e f f i c i e n c y i s t h e incentive f o r stayer/owners to increase t h e i r debt-equity r a t i o by r e m o r t g a g i n g i n o r d e r t o r e a l i z e m o r e b e n e f i t s from the s u b s i d y . T h i s type of c a p i t a l market incentive c o m p a t i b i l i t y problem i s not examined i n these s i m u l a t i o n s .  14.  W h i l e c o m m o n l y e m p l o y e d , t h e m o n e y m e t r i c d o e s h a v e some drawbacks. F o r example, B l a c k o r b y and D o n a l d s o n (1986) d e m o n s t r a t e t h a t money m e t r i c s a r e n o t c o n c a v e f o r arbitrary reference price vectors unless household preferences are homothetic.  15.  I t i s c o n c e i v a b l e t h a t some h o u s e h o l d s ' d e m a n d f o r h o u s i n g w i l l be a f f e c t e d b y t h e r e d u c t i o n i n e q u i v a l e n t e x p e n d i t u r e b r o u g h t a b o u t b y t h e new t a x b u r d e n . In t h a t c a s e , t o t a l t a x r e v e n u e s w i l l n o t be p r e c i s e l y e q u a l t o t h e t o t a l subsidy cost. The r e s u l t i n g f i s c a l i m b a l a n c e i s l i k e l y t o be s m a l l , p a r t i c u l a r l y i n t h e t r a n s a c t i o n s m o d e l , a n d s o i s tolerated.  16.  A v e r a g e owner renters.  17.  The p r e c e d i n g d i s c u s s i o n i m p l i c i t l y assumes t h a t t h e s u p p l y of h o u s i n g i s p e r f e c t l y e l a s t i c . As d i s c u s s e d i n t h e concluding chapter, the i n t r o d u c t i o n of a housing supply model i s a p r i o r i t y f o r f u t u r e r e s e a r c h . Until that research i s undertaken, p o l i c y p r e s c r i p t i o n s emerging from t h i s r e s e a r c h must be s e e n a s t e n t a t i v e .  *  second s i m u l a t i o n households.  income  is effected  i s $21,115,  by  setting  compared  /c(d) =  with  0 for  $16,854  for  147  VII. A.  Summary  and  Agenda  for  Future  Summary  The  object  of  this  d i s s e r t a t i o n has  test  e m p i r i c a l l y a model  of  used  to  related  tax  evaluate  reform  interest Of  shown  by  primarily  most  in  light  from  one  household's by  of  manifested  are  efficiency estimating  actual  this  and  both  since  Actual the  percent.  to  develop can  The of  in  and turn  be  hypothetical  mortgage  the  demand the  fall  well  The  the  however,  relocation  little  is  are  demand  confirms  this  equation  and  reforms.  i t becomes  reported  of  important demand  in  by  the  and  produced  by  earlier  considerably  small,  by  by  of  elasticities  range  housing  influenced  elasticity  conditional  within  is  tax  housing,  the  research  implications  housing  is  expenditures  very  specific  for  their  This  and  conditional  elasticities,  p r o b a b i l i t y of  the  of  and  relocate  The  research  adjust  another. to  in  this  to  status,  equity  elasticity.  research  works.  which  reforms.  prices  variables.  d i s t i n g u i s h between  the  current  i t s demographic  finding  In  to  introduction  households  willingness  economic  to  tax  i s the  dwelling  traditional  the  demand  p a r t i c u l a r i n t e r e s t throughout  relocating a  here  housing  been  deductibility.  consumption  that  housing  evaluated  reluctance  in  Research  lower  order  of  20  1 48  Household subsidy with of  into  such  immobility,  a  lump  sum  subsidies  9 percent  of  the tax l o s s ,  no  The  findings reported  are  relocation  much  less  households  Ideas  number  perfectly  relatively  For  could a  (with  t a x on  assets. subject  easy  grant,  context  that  here  most  equity one  and  may  similar  order  when  there  in the short the short  interest be  ( i n the  run.  run  deductibility  the case  were  in a  i s in place, i t  the model  compare  found  several  the  reform  i n t r o d u c t i o n of  in British Similarly,  Columbia, this  a p p l i e d t o examine on  possible  grounds.  to evaluate  realized goal  or a p p l i e d  that  Toronto.  r e v i s i o n s ) be  on  other  efficiency  wish  gains  built  i s to evaluate  and  to that  ambitious  be  Now  to evaluate  the c a p i t a l A more  can  obvious  of metropolitan some  would  associated  percent  particularly  than  tax reforms.  both  small  t o 42  suggest  loss  price  Research  The  example,  homeowner the  on  relatively  a  mobile.  presented  o f ways.  transform  deadweight  compared  also  consequential  model  proposals  here  can  i m p l i c a t i o n s of mortgage  housing-related is  The  disutilities),  for Future  The  grant.  i s therefore  are  distributional  in effect,  the sale  i s to specify  in  model  the e f f e c t s  of  a  of  housing  optimal  tax  reforms  to i n s t i t u t i o n a l constraints.  Whatever preferences  as  the reform, revealed  i t s evaluation  through  their  i s rooted  behavior  in  household  i n the market f o r  1 49  accommodation housing  another  sense  of  useful  data  how  changes.  of  are  the  the  the  of  a  one  of  vary  be  to  model  in  this  research.  unduly  restrict  in chapter  function,  chapter  s i x , may Further  The  impinge  for  household's  research.  relationship This  role  i s to  between would  one  of to  gain  model  a  depend  better  on  might  such  expect  can  another.  set  the  the  the of  actually  demographic  not for  of  useful  in  empirical  Expenditure demand social  cardinality  measures  of  in  social  determining  are. attributes  useful  in  another  thoroughly  characteristics  particularly  the  Linear  suggests  more  need  deductibility.  assumption  t h e r e f o r e be  next.  concerning,  Atkinson  resulting  relocate  at  housing  the  indexes  the  throughout  estimates  with  to  vary Secondly,  1  estimates  interest  Similarly,  household  prices  arrives  example,  investigate  be  to  data  in place  the  restrictions  propensity  That  this  for c o n s t r u c t i n g hedonic  For  upon  r e s e a r c h may  important  setting  mortgage  five.  together  s e r i o u s these  to  one  housing  c o n c l u s i o n s one  were  welfare  that  some p a r a m e t e r  restrictions  elasticity  one  test  estimates  and  from  Several  choice.  the  allow  reasons  urban has  change  fundamental  may  would  housing  one  quantity will  of  would  parameter  of  gain.  by  estimates.  nature  that  so  desirability  System  summarized  enquiry  the  portions  a  of  number  variables  however  example,  how  a  i n the  of  housing  alter  as  Doing  d r a m a t i c a l l y from  array  Note  set.  There  First,  the  line  critically  some c h a n g e s  quite  and  demand.  Another on  services,  and  determining line  of  the tenure  i f i t were  modelled  1 50  in  terms  more  of l i f e  explicit  demand  f o r housing  This housing,  the  White  and White  considerations  and  This  specific  policy  demonstrate  impinge  upon  work  need  exhibit  many  found  employee  in this  suspects  that  market.  to current  demographic  market  Indeed,  from  may  well  one w h i c h  may  be p u r s u e d here.  provide  a  n o t be  one employer  play  fruitful  a  do  between  by b u i l d i n g  to  differentials.  as they  the relationship  supply  includes a  salary  just  proposals.  reform.  variables  setting,  markets  developed  This  r e l u c t a n c e t o move  One  i n the labour  model.  where  t h e w e l f a r e and  of t h i s  markets  true  that  the a p p l i c a b i l i t y Labour  this  and long run  i s particularly  tax  to adjust  foundations  short  related  in order  enquiry;  s e t which i s  to develop  of a housing  to housing.  labour  i n the  numerous  be u s e f u l  f o r example,  next  housing  with  an e x p l i c i t  can s i g n i f i c a n t l y  characteristics  role  i t would  to evaluate  (1977),  effects  Finally,  the  a data  A  on t h e demand f o r  i s consistent  of housing.  i s t o be u s e d  demonstrable  by w e a l t h  given  exclusively  i n conjunction with  of the supply  confined  desirable,  focuses  Nonetheless,  2  model  efficiency  played  patterns.  comprehensive.  and i n so doing  model  and investment  of the role  i s also  research  precedents. demand  consumption  modelling  sufficiently  model  cycle  significant i nthe  the housing  line  for further  upon t h e  151  N O T E S TO  CHAPTER  SEVEN  F o r e x a m p l e , t h e h o u s i n g m a r k e t w i l l be q u i t e d i f f e r e n t b e t w e e n two s i m i l a r u r b a n a r e a s , w h e r e o n e a r e a i s e x p e r i e n c i n g s i g n i f i c a n t l y higher growth than the o t h e r . F o r a n e x p l a n a t i o n o f how u r b a n g r o w t h t r a n s l a t e s i n t o l a n d p r i c e s , see Capozza, H e l s l e y , and M i l l s (1986). For example; V e n t i and Wise (1984), K i n g (1983), Rosen ( 1 9 7 9 ) , a n d L a i d l e r ( 1 9 6 9 ) a l l f o c u s e x c l u s i v e l y on h o u s i n g demand. K i n g (1981), however, does i n t r o d u c e f i n i t e supply elasticities.  1 52  BIBLIOGRAPY  AARON,  H.J. (1972) S h e l t e r s and S u b s i d i e s Brookings I n s t i t u t i o n , Washington,  D.C.  A L B R I G H T , R., S. LERMAN, a n d C. MANSKI (1977) R e p o r t on t h e D e v e l o p m e n t o f an E s t i m a t i o n P r o g r a m f o r the M u l t i n o m i a l P r o b i t M o d e l , p r e p a r e d f o r t h e F e d e r a l Highway A d m i n i s t r a t i o n , O c t o b e r . 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MAYO ( 1 9 8 1 ) I n t r a u r b a n R e s i d e n t i a l M o b i l i t y : The R o l e o f T r a n s a c t i o n s Costs, Market Imperfections, and Household D i s e q u i l i b r i u m ; J Urban Econ, v o l . 9 , 332-348.  60.  pp.  WHITE, K . J . (1978) A G e n e r a l Computer Program f o r E c o n o m e t r i c Methods SHAZAM, E c o n o m e t r i c a , J a n u a r y , p p . 239-240.  --  158  Appendix Illustration  This  appendix 3  with  [p*  -  reference  empirical All  p  to  illustrates  *  the  chapters  of  variables  particular,  p*  ]/9/c  >  and  p  Using  LES  that  0  (1 )  Linear this  used  A  Expenditure  used  in  the  dissertation.  here  are  System  are  the  as  defined  maximum  and  in  the  minimum  text.  In  points,  * respectively,  S  =  [p|  of  the  p=(p  a  a  The is  linear  defined  V  (p s  V  where  ,p a  ,p a  Sa,  defined  ) and  expenditure  ,e)  =  /31n(x  -y s  ,e)  (p s a  system  ,e)  >  V  (p , e ) ] m a  introduced  =  b(/3)  +  ) +  (l-0)ln(e-p  a  7  , a  7  , and  x a  7  ln(e-p a  /3,  V  by  (2)  in chapter  three  by  a  (p m a  set  /c(d)  are  we  know  -7 a  ) -  -y s  /31np  c  )  (3)  c -  «(d)  and  b(/3)  (4)  a  parameters,  =  /31n/3 +  c  0-/3)ln(1-/3). From  (3)  and  (4)  that  V  (p s  1-/3 (e-p  -7 a s c x  )  ,e) a  > V  ( p ,e) m a  implies  /3 p  > a  (e-p  7 -7 a a c  )*exp[b(/3)-/31n(x  -7 )-/c(d)] s a  (5)  R e l a t i o n s h i p Between c ( ) and  f( )  160  To  simplify matters,  we  assume  here  that  7  =0.  This  a assumption chapter  i s consistent  five,  with  and a l l o w s  f(p  us  the empirical  to rewrite  results  reported  in  (5) a s  ) > c(/c(d))  (6)  a where  we  define 1-0 f(p  ) =  ( e - p x -y ) a s c  a  0 p  e(0,[e-7  p  a  ]/x ) c s  a  (7) and cU(d))  The  r e l a t i o n s h i p i n (6) i s i l l u s t r a t e d It  p  (e-7 )*exp[b(0)-01n(x -y ) - * ( d ) ] c s a  =  and  c a n be  that  shown  readily that  i t s maximum  value  Now  clear  define  from  (8) t h a t  )/x c  Then,  f o r values  increase  of  <  And  i tis  s  0.  in (1).  (9)  ] = c(/c(d)*)  i t i s clear  costs  causes  (p*-p ) t o increase,  * proposition  c'(/c(d))  .  of  s  «(d)>/e(d)*,  in transactions  the distance  )/x c  function  « ( d ) * by f[0(e-7  and  =0(e~7  i s at p a  immediately  12.  f ( p ) i s a concave a  a  an  in figure  (8)  from  c(«(d))  thereby  figure to  12  that  decrease,  confirming  the  Appendix Derivation  B  of  I(A  )  ii_  From  equation  3.30  i n the text,  I(A  ) i s defined  by  ji  I(A  ) = E(X ji  where  X  is a  |X i j  random  < A i j  )  (1 )  j i  v a r i a b l e which  adheres  to a  binomial  i j logistic  distribution.  The density  cumulative function  distribution  for X  f u n c t i o n and  respectively  probability  are given  by  i j  G(z)  =  1/F(z)  =  1/[1+exp(-z)]  g(z)  = G'(z) = exp(-z)/F  (2)  2  Therefore,  the expected  value  (z)  (3)  of  X  , given ij  I(A  ) = E(X ji  )/G(A i j  X  < A i j  , is  j i  )  J i 2  = F(A  ) \ ji  J  z exp(-z) G  (z) dz  (4)  162  To  solve  for  this  integral explicitly,  make  the  following  substitutions:  r  =  F(z)  r-1  =  exp(-z)  -ln(r-1) -dr/(r-1)  Then  4 can  I(A  be  ) =  rewritten  F(A  ji  Integrating  I(A  by  ) =  i n the  text.  z =  dz  as  r  ln(r-1)dr  (5)  oo  parts,  [1-F(A  ji  as  ) ^ j i  =  we  get  >]A - F(A )*ln[F(A )] j i j i j i j i  (6)  163  Appendix Variables  Table  I i n the text  regression This  Used  used  appendix  i n Hedonic  reports  to calculate  describes  C Regression  the results  our measure  the variables  of the hedonic  of housing  which  services.  a r e employed  i n that  regression. The  dependent  homeowner's value  estimate  first  subjective condition  ( i n $'000)  five  of s t r e e t s ,  playgrounds,  homeowner  with  satisfaction 1=completely we h a v e  dwelling  unit.  dwelling  X* 2 f 3 f • • f7#  These  unit's  market  with  homes,  1=excellent describes  which  BATHROOM  has X bedrooms,  by t h e  and 5=poor. the respondent's  on a s c a l e  of 1 to  satisfied.  on t h e d w e l l i n g  i s t h e number  i s a dummy  of parks  of shopping  and I n c o m p l e t e l y focus  regarding  number  are rated  the neighbourhood  dissatisfied  A n d BEDRMX  unit  SATISFCN  t h e homeowner's  environment  and q u a l i t y  variables  o f 1 t o 5, w i t h  variables  F o r example,  I provide  of other  of schools,  the variable  itself.  -  of h i sdwelling  in table  condition  quality  on a s c a l e  Next,  the  the l o gof the  of the neighbourhood  i n the area.  Similarly, overall  variables  evaluation  facilities  11,  i s LOGVALUE,  i n 1979. The  and  variable  o f bathrooms  variable,  BEDRMX=0  with  unit in  the  BEDRMX=1 i f  otherwise, f o r  1 64  The which  next  five  the dwelling  corresponding flats,  variables unit  parking  Also,  there  facilities  The electoral  final  i s located.  t o semidetached  and apartment  stories.  describe  buildings  district  o f more  are available  i n which  ZED506=1  i f the respondent  ZED506=0  otherwise.  These  housing,  i s a dummy  s e t o f dummy  the kind  of structure i n  a r e dummy  attached than  variable  variables  townhomes,  or l e s s  than s i x  to indicate  whether  on t h e p r e m i s e s .  variables the unit resides  correspond i s located.  t ot h e F o r example,  in electoral district  #506,  165  Appendix Two  As  discussed  solution linear  values  Solutions  i n the text,  Thus  the L i n e a r  one  f o r the n o n l i n e a r  approximations  indexes.  from  D  strategy model  f o r the d i r e c t  equations  Model  for  locating  entails  and  the  indirect  use  of  utility  5.3:  h A  =  l n ( e -p 7 - 7 ) m m a c  b(j3) +  m  )31np  -  K  (5.3a)  m for  m=o,r  h A  =  are  -7  /31n(x  s  s  replaced  with  ) +  -7  (1-/3)ln(x  a  c  equations  )  (5.3b)  c  5.8:  h A  =  b(/3) +  ln(e) -  m  ( p 7 +7 ) / e m a c m  -  01np  (5.8a) m  and h A  =  s  Domencich indexes and  -7  /3(lnx  s  in a  and  logit  so g u a r a n t e e s a  )  model  index,  so a  unique  (1975)  results  unique  restrictions  (5.8b)  s  McFadden  additional and  /x a  on  have  in a  solution.  shown  convex  that  i s not  of  likelihood  However,  our  the parameters appearing  solution  use  guaranteed.  linear  function  model  imposes  i n each These  166  restrictions equations indirect  stem  5.8  as  solutions  as  observe  our  (linear  utility  Estimation  to  from  i n t e r p r e t a t i o n of  approximations  the  l i n e a r i z e d model  characterized these  two  in  values  values  interpretations.  The  first  suggestive  of  traditional Note  for  whereby  /3  As  by  they  are  not that  perspective,  =  It  have  almost  A  in  household such  to  XI.  (column  0.64  sharply  and  as  are  two  distinct  is quite  interesting  identical  different  parameter  table  is  XI)  responses  to  price  expenditure.  indicates  a  zero,  in  the  in  the  the  regularity  conditions  likelihood  values  likelihood  value  the  model  and  household's  entirely (2)  with  contribute  interest not  0  suggests  discussed  secondary  direct  in  and  that  64  directed  changes  percent  in  of  towards  services.  which  do  the  leads  markedly  expenditures  approaches  decisions dictated  that  contrasts  B),  values  variables  household  (column  having  elastic  economic  accomodation This  of  highly  example  additional  despite  set  table  solutions  likelihood and  indexes  functions. of  that  of)  the  to  second  of  each  household's  household  these  context  of  thus  of  the  obtained  reported  in  are  table  not III  a  do  nonlinear  determinism  but  are  status.  this  values  results  housing  utility  solutions  s a t i s f a c t o r y from parameter  of  demographic  demographic  text,  set  are  only  research  because  (1)  theoretical not  model,  satisfy and  the  the  (3)  competitive in  of  text.  the  with  the  TABLE Two S e t s Estimates for  Parameter  XI  of Parameter the Linear Model  Solution n *n  Solution "B"  .64229  .01405  v  .72861  1.1780  1  -287.86  810.80  41 1 2 0  1 475  .95917  1 .3521  0.0(F)  0.0(F)  343.77  -692.9  99.261  -808.5  •82.547  394.60  kl  kw  kn  -log  L  75.057  74.114  168  Appendix Summary  The model the  following  described  tenure  of C r o s s t a b u l a t i o n s  demographic  in chapter  choice  E  variables  five,  play  a  particularly  with  i f age  of  household  head  i s less  Dw=1  i f age  of  household  head  i s married  and  years,  otherwise,  Dw=0;  than  These  variables  major  regards  10  than  43,  otherwise,  has  been  for  of  to  D1=0; less  and  were of  findings  selected  on  residential of  these  the  b a s i s of e x p l o r a t o r y  mobility  by  crosstabs are  demographic  summarized  H o u s e h o l d Head  (xhage)  *  For  14  of  the  19 m o v e r / r e n t e r s  *  For  11  of  the  12 m o v e r / o w n e r s  *  For  65  of  the  107  stayers  i n our i n our  i n our  sample, sample,  sample,  xhage<36 xhage<43  xhage>42.  status.  briefly  here.  Age  i n the  size.  crosstabulations The  role  decision:  Dl=1  Dn=household  key  169  Marital *  16  Status  of the  17 m o v e r s less  *  A l l of the  who  were  than  or  *  4 t h e 31  movers  *  A l l recently  none had  been  to 9  years  have  been  married  had  been  recently  widowed  have  equal  12 m o v e r / o w n e r s and  married  married for  at  least  once,  separated  been  household  divorced.  heads  (male o r  female)  are  stayers.  Household  Size  (xnhh)  *  For a l l of  the  19 m o v e r / r e n t e r s ,  *  F o r a l l of  the  12 m o v e r / o w n e r s ,  *  20  o f t h e 31  Previous  *  Of  the  movers  had  xnhh<7  children  over  7 years  of  age.  Tenure  19 m o v e r / r e n t e r s , owner  For 7 of  the  10 w e r e  occupiers,  presumably *  no  xnhh<5  renters,  and  7 were  neither  a r e newly  formed  households)  12 m o v e r / o w n e r s , occupied  previously  the previous  accomodation  tenure  2  were  (and so  was  owner  170  Appendix  F  Deadweight  This  appendix  expression  identifies  f o r deadweight  DL(p 2  is  non-negative,  price  p  , for p 2,  V(p 1  For  the c o n d i t i o n s  < p  which the  ) = T L ( p ) - EG(p ) 2 2  , where p 1  gain  under  loss  and i s a d e c r e a s i n g  2 _  Equivalent  Loss  (1)  function  of the p o s t - r e f o r m  and e a r e g i v e n .  1 (EG) i s d e f i n e d  implicitly  by  ,e+EG) = V ( p ,e) = v 2 2  e x p o s i t i o n a l ease,  we  define  (2)  the f o l l o w i n g  partial  derivatives:  V ' (p) = 9 V ( p 2  V  • (e) =  ^V(p  2 V 1  Thus,  ,e)/?p  2  , e V d e  2 '(EG) = ^ ) V ( p ,e+EG)/*£(e+EG) 1  taking  respect  2  the p a r t i a l  to p  yields 2  d e r i v a t i v e of both  sides  o f (2) w i t h  171  V  1  1 —>  ( E G ) * EG'(p ) = V '(p) 2 2  EG'(p ) = 2  [V ' ( p ) / V ' ( e ) ] 2 2 =  Similarly,  tax loss  -x * 2  TL'(p  ) =  p  i s clear  .  As p  =p 2  1  2  )x  (4) 2  falls  equations  (5)  1, 2, a n d 4 t h a t  ( i e , as the rate  of subsidy  DL=0  when  increases), the  (p -p 1 2  Looking Marshall  money  i s best  '(e) = V 2  loss  i s given  by  ) = T L ' ( p ) - EG'(p ) 2 2  =  )*x 2  '(p ) + x * 2 2  at equation  6  i t is difficult  i n h i s assumption represented  '(EG),  a n d we  [V * ( e ) / V '(EG) 2 1  that  the marginal  by a c o n s t a n t . could  not t o  declare  1] ( 6 )  sympathize utility  For i n that  unambiguously  of  event that  1  DL'(p  )<0 2  is  from  i n deadweight  DL'(p  V  by  2  change  with  (p -p 1 2  (3)  ( p -p )*x ' ( p ) - x 1 2 2 2 2  2 It  =  [V ' ( e ) / V '(EG)] 2 1  [V ' ( e ) / V ' ( E G ) ] 2 1  i s defined  TL  *  f o r p >p provided 2 1  downward s l o p i n g .  that  the marshallian  demand  curve  172  As  i t i s , however,  equation partial  6  the  is positive.  derivatives  term  on  the r i g h t  T o -see t h i s ,  are evaluated  note  a t V(  hand  from  ) = v  side  1 that  .  Thus  of both  we  know  2 that  V  '(e) > V 2  further  '(EG)  i n the post  conclude  therefore  increase  with  "income  since  a  little  the  effect"  reform i s that  size  of  subsidized  income  state.  the deadweight the  ( i e , the r a t i o  subsidy, [V  The  loss  but  '(e)/V 2  large.  extra  will  go  most  we  1  is likely  will  '(EG)]) 1  n o t do  so  becomes  can to i f the too  


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