Discussion of
“From Shirtsleeves to Shirtsleeves in a Long Lifetime”
by Nobu Kiyotaki, Alex Michaelides and Kalin Nikolov
Dirk Krueger
University of Pennsylvania, CEPR, and NBER
Conference in Honor of Ed Prescott
Tokyo, November 3, 2006
Purpose of the Paper
• Construction of a quantitative theory that
— captures the life cycle profile of the buying/renting decision
— allows to study the determinants of house price changes (financial
constraints, productivity growth etc.)
The Paper: Overview
• Land as fixed factor in production of structures
• Collateral constraints
• Preference for buying over renting
Relationship Between Model Elements and Desired Results
Model Elem.\Questions
Land as Fixed Factor
Collateral Constraint
Buy Preference
Life Cycle
Not Needed
Needed
Needed
Price Changes
Needed
Needed
Not Needed
Question 3
Needed
Needed
Needed
Key Model Elements: Technology
• Final output production
η
Ct + It = Yt = (AtNt)1−η ZY,t
• Production of structures
ZY,t + ZR,t = Zt = Ktγ L1−γ
• Capital accumulation
Kt+1 = (1 − δ)Kt + It
Key Model Elements: Population and Endowments
• Households can be in one of five states: low (εl ), medium (εm) and
high (εh) productivity, retired and dead. Transition matrix given by
today\tom
εl
εm
εh
εl
ω(1 − δl )
ωδl
0
εm
0
ω(1 − δm) ωδm
0
0
ω
εh
retired
0
0
0
dead
0
0
0
retired dead
1−ω
0
1−ω
0
1−ω
0
σ
1−σ
0
1
• GN − ω newborns of low productivity. GN = Nt/Nt−1 is population
growth rate.
Key Model Elements: Preferences
• Standard time-separable expected utility with time discount factor β
• Period utility function
u(ct, ht)
if household owns
u(ct, (1 − ψ)ht) if household rents
Key Model Elements: Financial Market Structure
• Only financial asset is shares in real estate mutual fund (risk-free).
Number of shares denoted by st.
• Collateral constraint for home owners buying house of size ht
θqtht ≤ qtst
where θ can be interpreted as downpayment requirement.
• Households may be renters, constrained homeowners or unconstrained
homeowners.
Main Results I: Life Cycle Profiles
• Young, low productivity households do not find it optimal to save.
Thus they remain renters and consume what they earn. Wait for
productivity increase. Wear shirtsleeves.
• Middle productivity households are first renters that save for downpayment. Then they become credit-constrained owners that expand
their homes and finally become unconstrained owners. Same for high
productivity households (do we need those?).
• Retired households decumulate wealth since interest rate in general
equilibrium is low, relative to time discount rate. Wear (less fashionable) shirtsleeves.
Productivity increase, constrained house purchase
1.6
1.4
housing
1.2
1
0.8
shares
0.6
0.4
0.2
Unconstrained
Retirement
0
1
5
9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
Main Results II: Changes in Price of Real Estate
(Steady State Comparisons)
• Financial constraints important for home ownership rates, but not for
real estate prices and quantities (mainly reallocation among owners
and renters).
• Increase in the importance of land in the production of structures:
Large increase in housing prices and house price to rent ratios. This
finding could be exploited empirically, both in a country cross-section
and a time series within a country.
Table 5
Column
% of tenants
% of constrained households
% of unconstrained homeowners
% of shares owned by tenants
% of shares owned by constrained
% of housing used by tenants
% of housing used by constrained
Current account as % of GDP
Net foreign Assets as % of GDP
Value of total structures to GDP
Housing structures to total structures
Value of housing to wages
Housing price to rental rate
Real return
House price (N=An=1)
Output (N=An=1)
baseline
1
θ=0.1
2
θ=1.0
3
gn=1.02
4
ga=1.03
5
b=0.1
6
S*=0
7
γ=0.5
8
24.76
8.27
66.97
0.08
0.33
8.61
2.42
0.90
-19.49
2.98
0.45
2.50
8.65
6.62
1.66
1.11
2.59
25.49
71.92
0.02
0.36
0.76
8.05
0.89
-19.32
2.98
0.45
2.50
8.66
6.61
1.66
1.11
37.32
11.83
50.85
0.80
3.15
13.87
6.99
0.86
-18.77
2.99
0.45
2.50
8.69
6.58
1.66
1.11
42.35
11.76
45.88
0.93
3.73
17.26
8.30
1.93
-34.76
3.00
0.45
2.48
8.77
7.27
1.71
1.10
38.77
14.95
46.28
1.06
4.10
15.44
9.12
2.17
-42.69
2.83
0.45
2.35
8.31
7.69
1.67
1.09
21.10
15.12
63.78
1.07
2.70
6.74
5.98
0.14
-3.17
3.33
0.45
2.74
9.61
5.86
1.78
1.12
36.85
10.99
52.17
0.87
2.93
13.53
6.40
0.00
0.00
2.90
0.46
2.46
8.43
6.84
1.63
1.10
25.34
5.54
69.12
0.07
0.28
7.87
1.90
8.12
-137.70
5.18
0.48
4.49
13.89
7.54
4.95
0.89
γ=0.5
9
12.84
11.09
76.06
0.16
0.47
3.47
3.09
0.93
-13.26
4.49
0.51
4.22
11.86
8.64
4.40
0.88
A Great Question Their Model could Address
• Substantial population aging predicted for the industrialized world. In
many regions population will be shrinking (absent a change in migration policy).
• Question: what the impacts of this massive change on the (future)
price of real estate and the fraction of households renting. Who is
gaining, who is losing?
• Note: to answer this important question one needs exactly all three
elements of their model
population growth rate
0.03
US
European Union
Rest OECD
Rest World
0.025
0.02
popgr
0.015
0.01
0.005
0
−0.005
−0.01
2000
2010
2020
2030
2040
Year
2050
2060
2070
2080
working age population ratio
US
European Union
Rest OECD
Rest World
0.85
wapr
0.8
0.75
0.7
0.65
0.6
2000
2010
2020
2030
2040
Year
2050
2060
2070
2080
Conjectured Results
• Decline in the price of real estate
• Decline in the value of land; capital loss for the owners of land
• But: when does this decline start? Of course depends on when the
severe aging of population enters information set of households.
• Their model is a perfect laboratory to answer these questions.