Housing Price, Mortgage Lending and Speculative Bubble: a
UK perspective
Dr Qin Xiao
University of Aberdeen Business School
Contents1. Introduction2. Model3. Empirical Investigations4. Tentative Conclusions
1. Introduction
Introduction Experiments in laboratory asset markets suggest
that When an asset market involves a large number of
uninformed and inexperienced participants, bubble is a standard state of affairs.
As bubble arises, even the informed and experienced traders may also ride on the bubble. (Smith, Suchanek et al. 1988; Caginalp, Porter et al. 1998; Caginalp, Porter et al. 2000a; Caginalp, Porter et al. 2000b; Caginalp, Porter et al. 2001)
Such observations call for modifications to the conventional analytical framework which assumes that asset markets are continuously efficient.
Introduction Speculative asset price bubble is potentially an
interesting topic to both policy makers and market investors
Although they may not use the term “bubble” when talking about one.
Investors are interested in making the most out of a bull market, without being stranded when the bubble deflates
It is also an important issue for the policy makers, although most of them are so far reluctant to face it.
Introduction The bubble literature can be roughly
divided into three strands. i. To prove or disprove the existence of a
bubble in an asset price.
ii. To measure the proportion of that price which is purely bubble.
iii. To forecast How fast the bubble increases How likely the bubble will burst in the next
period; When the bubble is purged eventually, in
what manner will that happen?
2. Model
Model Model is based on (Caginalp and
Ermentrout 1990; and Caginalp and Balenovich 1999)
Model Assumptions prices adjust as a result of excess
demand; excess demand depends on the relative
supply of the housing to the mortgage supply, both finite though not fixed;
The supply of the mortgage is a function of the price dynamics
Model Each unit of wealth is in one of two states:
housing or cash. The fraction of the wealth in housing asset
is
tMtPtN
tPtNtB
(1)
Model Participants are both housing and
cash holders. At any time, a typical investor will
buy housing with probability k and sell it with probability 1-k
Hence, the flow demand function for housing
And the flow supply function tBktD 1
tBktS 1
(2)
(3)
Model k is a function of investor sentiment, (t). with (t) driven by two forces: trend following and
mean reverting
0&0
11
1
21
02
01
21
qqwith
dt
tdP
tPdt
tdP
tPq
dt
tdP
tPq
ttt
f
f
(5)
Model 1: Bubble generation mechanism 2: price correction mechanism
Price Dynamics
10
tS
tD
tS
tStD
dt
tdP
tP
(6)
Model Substitute equation 1 - 5 into 6, and
define
tNtM
tL
(7)
1
112
121
1
2
1
P
L
d
dP
Pd
dP
Pq
d
dP
Pq
d
dP
P
f
f
0
tdtd
01 LP
Model Assume the dynamics of the liquidity
d
dP
Pd
dL
L
11 (8)
P relax borrowing constraint
L
3. Empirical Investigations
Empirical Questions How much of the house price and
mortgage growth in UK can be explained by this model?
The model implies two forces are at play: one is a stabilizer, the other destabilizer What is the empirical evidence on the
relative strengths of the two?
UK House Price ( RPI deflated 1975=100)
70.00
90.00
110.00
130.00
150.00
170.00
190.00
210.00
230.00
250.00
270.0019
75 Q
1
1976
Q3
1978
Q1
1979
Q3
1981
Q1
1982
Q3
1984
Q1
1985
Q3
1987
Q1
1988
Q3
1990
Q1
1991
Q3
1993
Q1
1994
Q3
1996
Q1
1997
Q3
1999
Q1
2000
Q3
2002
Q1
2003
Q3
2005
Q1
2006
Q3
Adjust scale
Show log changes
UK House Price and GDP
80.00
100.00
120.00
140.00
160.00
180.00
200.00
220.00
240.00
260.00
280.0019
75 Q
1
1976
Q4
1978
Q3
1980
Q2
1982
Q1
1983
Q4
1985
Q3
1987
Q2
1989
Q1
1990
Q4
1992
Q3
1994
Q2
1996
Q1
1997
Q4
1999
Q3
2001
Q2
2003
Q1
2004
Q4
2006
Q3
1975
Q1
= 10
0
Real house price
Real GDP
UK House Price and Housing Loan (RPI deflated 1975Q1=100)
70.00
90.00
110.00
130.00
150.00
170.00
190.00
210.00
230.00
250.00
270.00
Hous
e pr
ice
80.00
180.00
280.00
380.00
480.00
580.00
680.00
Hous
ing
loan
House price
Housing loan
Building the Statistical Model The fundamental price: approximated by
GDP. The liquidity: approximated by housing
loan Cross products between pairs of
regressors implied by the model are also examined.
Variables are deflated by RPI if appropriate The regressors are selected using stepwise
regressions.
Building the Statistical Model
VE
E
Xy ttt
'
0
Building the Statistical Model
t
tt l
py
411111
31
0000
0000000
ttttttt
ttttt pplllll
llpgdpx
T
7654321
4321
0000
0000000
t
tt
1
1log
t
tttt X
XXXx
V
Building the Statistical Model It is possible that agents in the housing
and/or the mortgage market behave asymmetrically in different phases of a market cycle.
ttt
t
tt
sss
s
st
stt
VE
E
Xy
'
0
Building the Statistical Model St: a state variable following a first-order
two-state Markov chain, with transition probabilities
2,1,
Pr
,...,,Pr
1
111
ji
q
isjs
isisjs
ij
tt
tttt
Model Estimation Four models are estimated by assuming no-switching and 0 (no switching
SUR) With switching and 0 (Markov-
switching SUR) No witching and = 0 (no switching
single) With switching and = 0 (Markov-
switching single)
Model Comparison
Table 1 R Squares Markov-switching
SUR No-switching SUR
Markov-switching single
No-switching single
Price 0.703 0.663 0.675 0.675 Loan 0.560 0.591 0.703 0.606 Overall 0.563 0.593 0.703 0.607
Model Comparison
Table 1 Model Ranking Based on In-sample Sum of Squared Errors By price model By mortgage model Overall
1 Markov-switching SUR
Markov-switching single
Markov-switching single
2 Markov-switching single
No-switching single
No-switching single
3 No-switching single No-switching SUR
No-switching SUR
4 No-switching SUR
Markov-switching SUR
Markov-switching SUR
Parameter EstimatesMarkov-switching Single
Dependant Variable = Price
State one State two Coefficient
estimates t ratio Coefficient
estimates t ratio
gdp(t) 0.67 0.29 0.68 0.29 price(t-1) 0.62 1.11 0.62 1.11 loan(t) 0.04 1.94 0.04 1.94 loan(t-3) 0.04 4.17 0.04 4.18
Dependant Variable = Mortgage
loan(t-1) -0.52 -0.58 -0.07 -0.11 loan(t-2) -0.47 -0.62 -0.46 -0.93 loan(t-3) -0.71 -0.67 -0.42 -0.59 loan(t-5) -0.70 -1.44 -0.23 -0.71 loan(t-6) 0.04 0.08 -0.26 -0.83 price(t) 2.40 0.17 2.12 0.22 price(t-4) -0.47 -0.03 -1.66 -0.18
Price is meanreverting
distablizer
Probabilities of the States
Probability of State One (House price)
0.6
0.602
0.604
0.606
0.608
0.61
0.612
Probabilities of the States
Probability of State One (Housing loan)
0
0.2
0.4
0.6
0.8
1
1.2
1977
Q2
1978
Q4
1980
Q2
1981
Q4
1983
Q2
1984
Q4
1986
Q2
1987
Q4
1989
Q2
1990
Q4
1992
Q2
1993
Q4
1995
Q2
1996
Q4
1998
Q2
1999
Q4
2001
Q2
2002
Q4
2004
Q2
2005
Q4
2007
Q2
Diagnostic Check
House Prices and Fitted Values (MS single)
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
1977 Q
2
1979 Q
1
1980 Q
4
1982 Q
3
1984 Q
2
1986 Q
1
1987 Q
4
1989 Q
3
1991 Q
2
1993 Q
1
1994 Q
4
1996 Q
3
1998 Q
2
2000 Q
1
2001 Q
4
2003 Q
3
2005 Q
2
2007 Q
1
House price
Phat
Diagnostic CheckHousing Loans and Fitted Values (MS single)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1977 Q
2
1979 Q
1
1980 Q
4
1982 Q
3
1984 Q
2
1986 Q
1
1987 Q
4
1989 Q
3
1991 Q
2
1993 Q
1
1994 Q
4
1996 Q
3
1998 Q
2
2000 Q
1
2001 Q
4
2003 Q
3
2005 Q
2
2007 Q
1
Y1
YHATJ
Diagnostic CheckStandardized Residuals (House price)
-4.1
-3.1
-2.1
-1.1
-0.1
0.9
1.9
2.9
3.9
Resi_ms_sur
Resi_sur
Resi_ms
Resi
L
U
Diagnostic Check
Standardized Residuals (Housing loan)
-4
-3
-2
-1
0
1
2
3
4
5
Resi_ms_sur
Resi_sur
Resi_ms
Resi
L
U
Work remains Use a convergence measure to investigate the
forecast power of the model The significance level of the Markov-switching
model is to be established using Monte Carlo experiments
Simulate the time paths of house price and housing loans implied by the statistical model to illustrate The origin of the bubble The propagation mechanism of the bubble The stability of the system
4. Tentative Conclusions
Tentative Conclusions We have investigated a model in which a
housing price bubble arises as a result of trend following sentiment
The model takes into account of the feedback effects between housing prices and mortgage lending;
It also accounts for changing sentiment in the market
The application of this model to UK housing market confirms that the model roughly explains 70% of the overall variations of both prices and housing loans.
The significance and forecast ability of the model are still to be established
The End
Thank you!
Comments?