文档介绍：House Prices,
Residential Mortgage Credit
and ary Policy
Meenakshi Basant Roi
Rhys Mendes
Preliminary
December 2004
Objectives
• Should the Bank respond to house price
growth?
• Use model with a financial accelerator in
household sector to answer this question
• Answer this question in the presence of
deviations from fundamentals
Outline
• Baseline Model
• Model assessment
• Deviation from fundamental experiment
• Policy parison
Related Literature
• Household Financial Accelerator:
qAoki et al. (2002)
qIacoviello (2004)
Model Overview
• 2 types of households: patient and
impatient
• Financial intermediary
• House producers
• Intermediate good producers
• Final good producers
• ary authority
Patient Consumers
¥
t p p p
max Et β p [log Ct+ j + γ log H t+ j + ξ log(1­ Lt+ j )]
C p ,H p ,Lp ,B å
t t+1 t t+1 j=0
subject to:
æ H p ö
P C p + Q H p ­ (1­δ)H p + Q Fç t+ j+1 ÷H p + D + T p
t+ j t+ j t+ j ( t+ j+1 t+ j ) t+ j ç p ÷ t+ j t+ j+1 t+ j
è Ht+ j ø
p p
= Wt+ j Lt+ j + Rt+ j Dt+ j +Vt+ j
where:
2
æ H p ö φæ H p ö
Fç t+ j+1 ÷ = ç t+ j+1 ­1÷
ç p ÷ ç p ÷
è Ht+ j ø 2 è Ht+ j ø
Impatient Consumers
¥
t i i i
max Et βi [log Ct+ j + γ log H t + j +ξ log(1­ Lt+ j )]
Ci ,H i ,Li ,B å
t t+1 t t+1 j=0
subject to:
æ H i ö
P C i + Q H i ­ (1­δ)H i + Q Fç t + j+1 ÷H i + Z B
t + j t+ j t + j ( t+ j+1 t + j ) t + j ç i ÷ t + j t+ j­1 t+ j
è H t+ j ø
i
=Wt+ j Lt + j + Bt + j +1
In equilibrium:
æ B ö
Z =ψç t + j+1 ÷R
t + j ç Q H ÷ t + j
è t + j t+ j+1 ø
House Producers
Evolution process for housing stock:
Ht+1 ­ (1­δ)Ht = F(It , It­1)
2
é ηæ I ö ù
F(I , I ) = ê1­ ç t ­1÷ úI
where t t­1 2 ç I ÷ t
ëê è t­1 ø ûú
House producers’ profit maximization problem:
¥
j p
max Et β p λt+ j [Qt + j F(It+ j , It+ j­1 )­ Pt + j It+ j ]
I å
t j=0
Final Good Producer
• Technology:
ε
é 1 ε­1 ù ε­1
Y = Y z ε dz
t êò t ( ) ú
ë 0 û
• Profit maximization impli