Housing Price, Mortgage Lending and Speculative Bubble: a UK perspective Dr Qin Xiao University of Aberdeen Business School [email protected]

Housing Price, Mortgage Lending and Speculative Bubble: a

UK perspective

Dr Qin Xiao

University of Aberdeen Business School

[email protected]

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)

QIN XIAO

N(t): the units of housing; P(t): the price of the housing; M(t): the value of the cash.

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)

QIN XIAO

Pf(t) is the fundamental price of housing asset at time t.

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



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!

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Documents

Housing Price, Mortgage Lending and Speculative Bubble: a UK perspective Dr Qin Xiao University of Aberdeen Business School [email protected]