Introduction
Modelling Asymmetric Cycles in Housing Markets
The Econometric Model
Data and Estimation Results
Estimation Results
London | Super prime | Tier 1 | Tier 2 | Inner London | Outer London | |
---|---|---|---|---|---|---|
Estimated parameters | ||||||
ϕ0 | \( {\displaystyle \begin{array}{c}{0.666}^{\ast}\\ {}(0.062)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.091}^{\ast}\\ {}(0.073)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.235}^{\ast}\\ {}(0.021)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.467}^{\ast}\\ {}(0.080)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.435}^{\ast}\\ {}(0.025)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.106}^{\ast}\\ {}(0.012)\end{array}} \) |
ϕ1 | \( {\displaystyle \begin{array}{c}{1.799}^{\ast}\\ {}(0.047)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.320}^{\ast}\\ {}(0.028)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.383}^{\ast}\\ {}(0.013)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{1.053}^{\ast}\\ {}(0.040)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.574}^{\ast}\\ {}(0.023)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.766}^{\ast}\\ {}(0.022)\end{array}} \) |
ϕ2 | \( {\displaystyle \begin{array}{c}-{0.856}^{\ast}\\ {}(0.079)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.171}^{\ast}\\ {}(0.039)\end{array}} \) | \( {\displaystyle \begin{array}{c}-0.031\\ {}(0.021)\end{array}} \) | \( {\displaystyle \begin{array}{c}{2.585}^{\ast}\\ {}(0.096)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.330}^{\ast}\\ {}(0.039)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.500}^{\ast}\\ {}(0.044)\end{array}} \) |
ϕ3 | \( {\displaystyle \begin{array}{c}{0.242}^{\ast}\\ {}(0.063)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.785}^{\ast}\\ {}(0.039)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.548}^{\ast}\\ {}(0.021)\end{array}} \) | \( {\displaystyle \begin{array}{c}-2{.510}^{\ast}\\ {}(0.094)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.223}^{\ast}\\ {}(0.041)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.448}^{\ast}\\ {}(0.046)\end{array}} \) |
ϕ4 | \( {\displaystyle \begin{array}{c}-{0.192}^{\ast}\\ {}(0.038)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.357}^{\ast}\\ {}(0.026)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.168}^{\ast}\\ {}(0.013)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.088}^{\ast}\\ {}(0.041)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.154}^{\ast}\\ {}(0.025)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.150}^{\ast}\\ {}(0.023)\end{array}} \) |
θ0 | \( {\displaystyle \begin{array}{c}-{0.434}^{\ast}\\ {}(0.130)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{1.459}^{\ast}\\ {}(0.128)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.085}^{\ast}\\ {}(0.035)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.467}^{\ast}\\ {}(0.111)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.353}^{\ast}\\ {}(0.161)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.215}^{\ast}\\ {}(0.066)\end{array}} \) |
θ1 | \( {\displaystyle \begin{array}{c}-{1.146}^{\ast}\\ {}(0.090)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.350}^{\ast}\\ {}(0.076)\end{array}} \) | \( {\displaystyle \begin{array}{c}0.026\\ {}(0.065)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{1.053}^{\ast}\\ {}(0.035)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.400}^{\ast}\\ {}(0.107)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.034}^{\ast}\\ {}(0.035)\end{array}} \) |
θ2 | \( {\displaystyle \begin{array}{c}{1.746}^{\ast}\\ {}(0.134)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.216}^{\ast}\\ {}(0.040)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.485}^{\ast}\\ {}(0.037)\end{array}} \) | \( {\displaystyle \begin{array}{c}{2.585}^{\ast}\\ {}(0.101)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.862}^{\ast}\\ {}(0.093)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.229}^{\ast}\\ {}(0.075)\end{array}} \) |
θ3 | \( {\displaystyle \begin{array}{c}-{0.585}^{\ast}\\ {}(0.091)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.428}^{\ast}\\ {}(0.051)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.862}^{\ast}\\ {}(0.065)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{2.510}^{\ast}\\ {}(0.099)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.923}^{\ast}\\ {}(0.314)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.454}^{\ast}\\ {}(0.088)\end{array}} \) |
θ4 | \( {\displaystyle \begin{array}{c}-0.058\\ {}(0.057)\end{array}} \) | \( {\displaystyle \begin{array}{c}-0.019\\ {}(0.048)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.349}^{\ast}\\ {}(0.026)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.018}^{\ast}\\ {}(0.045)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.473}^{\ast}\\ {}(0.051)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.266}^{\ast}\\ {}(0.047)\end{array}} \) |
γ1 | \( {\displaystyle \begin{array}{c}-{2.950}^{\ast}\\ {}(0.191)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{7.400}^{\ast}\\ {}(0.276)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{5.400}^{\ast}\\ {}(0.499)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{0.950}^{\ast}\\ {}(0.166)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{6.900}^{\ast}\\ {}(0.258)\end{array}} \) | \( {\displaystyle \begin{array}{c}-{1.650}^{\ast}\\ {}(0.257)\end{array}} \) |
γ2 | \( {\displaystyle \begin{array}{c}{1.204}^{\ast}\\ {}(0.109)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.543}^{\ast}\\ {}(0.291)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.012}^{\ast}\\ {}(0.545)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.300}^{\ast}\\ {}(0.139)\end{array}} \) | \( {\displaystyle \begin{array}{c}{2.451}^{\ast}\\ {}(0.265)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.592}^{\ast}\\ {}(0.099)\end{array}} \) |
c | \( {\displaystyle \begin{array}{c}{2.156}^{\ast}\\ {}(0.094)\end{array}} \) | \( {\displaystyle \begin{array}{c}{4.422}^{\ast}\\ {}(0.178)\end{array}} \) | \( {\displaystyle \begin{array}{c}{1.018}^{\ast}\\ {}(0.545)\end{array}} \) | \( {\displaystyle \begin{array}{c}{0.307}^{\ast}\\ {}(0.025)\end{array}} \) | \( {\displaystyle \begin{array}{c}{5.582}^{\ast}\\ {}(0.110)\end{array}} \) | \( {\displaystyle \begin{array}{c}{5.376}^{\ast}\\ {}(0.026)\end{array}} \) |
Diagnostic tests (p values) | ||||||
Test for Corr. | 0.255 | 0.278 | 0.479 | 0.670 | 0.198 | 0.120 |
Test for no Rem. Asy. | 0.556 | 0.358 | 0.706 | 0.903 | 0.862 | 0.775 |
Test for Par. Const. | 0.346 | 0.382 | 0.414 | 0.385 | 0.373 | 0.350 |
Dissecting London’s Housing Market Cycle
Identifying House Price Cycles
Expansion | Contraction | |
---|---|---|
Duration | 15.85 | 5.07 |
Amplitude | 0.10 | −0.20 |
Cumulation | 1.86 | −0.29 |
Excess | 0.03 | −0.09 |
Monte Carlo Simulation Experiment
Model | Duration | Amplitude | Cumulation | Excess | ||||
---|---|---|---|---|---|---|---|---|
Contr. | Expan. | Contr. | Expan. | Contr. | Expan. | Contr. | Expan. | |
Data | 5.07 | 15.85 | −0.20 | 0.10 | −1.86 | 0.29 | 0.03 | −0.09 |
RW | 7.33 | 10.66 | −0.07 | 0.04 | −0.45 | 0.06 | 0.002 | −0.004 |
AR(p) | 5.57* | 16.14* | −0.13 | 0.09* | −0.95 | 0.05 | 0.004 | −0.001 |
AR-GARCH(1,1) | 10.21 | 20.42 | −0.22 | 0.31 | −2.53* | 0.97 | 0.006 | −0.001 |
LSTAR | 5.86* | 16.42* | −0.05 | 0.09* | −10.8 | 0.20 | 0.003 | −0.01 |
GSTAR | 5.91* | 15.20* | −0.22* | 0.08* | −1.30 | 0.33* | 0.02* | −0.03 |
Forecasting House Prices
Point Forecasts Measures
Density Forecast Measures
Forecast horizon | Forecast error measure | AR(p) | LSTAR | GSTAR | AR GARCH(1,1) |
---|---|---|---|---|---|
PANEL A: Point forecasts | |||||
1 | MFE | 0.009 | 0.006 | 0.002 | 0.005 |
3 | 0.012 | 0.011 | 0.004 | 0.008 | |
6 | 0.014 | 0.013 | 0.009 | 0.009 | |
12 | 0.016 | 0.019 | 0.012 | 0.011 | |
1 | sMAE | 0.008 | 0.009 | 0.004 | 0.005 |
3 | 0.012 | 0.010 | 0.006 | 0.006 | |
6 | 0.011 | 0.011 | 0.009 | 0.008 | |
12 | 0.015 | 0.012 | 0.0012 | 0.010 | |
1 | mRAE | 1.000 | 1.008 | 0.995 | 0.994 |
3 | 1.000 | 1.012 | 1.003 | 1.004 | |
6 | 1.000 | 1.013 | 1.005 | 1.005 | |
12 | 1.000 | 1.023 | 1.007 | 1.007 | |
1 | RMSPE | 0.004 | 0.003 | 0.003 | 0.003 |
3 | 0.005 | 0.004 | 0.004 | 0.005 | |
6 | 0.008 | 0.005 | 0.005 | 0.006 | |
12 | 0.009 | 0.007 | 0.006 | 0.007 | |
PANEL B: Density forecast | |||||
1 | LogS | 0.000 | 0.001 | 0.001 | 0.000 |
3 | 0.001 | 0.001 | 0.001 | 0.001 | |
6 | 0.001 | 0.001 | 0.002 | 0.001 | |
12 | 0.002 | 0.002 | 0.002 | 0.002 | |
1 | QRS | 0.003 | 0.002 | 0.002 | 0.003 |
3 | 0.003 | 0.003 | 0.003 | 0.004 | |
6 | 0.004 | 0.003 | 0.003 | 0.004 | |
12 | 0.004 | 0.004 | 0.004 | 0.005 | |
1 | CRPS | 2.051 | 1.992 | 1.877 | 1.984 |
3 | 2.189 | 2.078 | 1.922 | 1.994 | |
6 | 2.452 | 2.219 | 2.004 | 2.000 | |
12 | 2.557 | 2.267 | 2.015 | 2.002 | |
1 | qS | 0.021 | 0.022 | 0.021 | 0.022 |
3 | 0.025 | 0.026 | 0.025 | 0.024 | |
6 | 0.037 | 0.029 | 0.034 | 0.029 | |
12 | 0.039 | 0.037 | 0.034 | 0.034 |
Is London Different from Other Cities?
City | Nonlinearity test | Dynamic symmetry |
---|---|---|
p-value | p-value | |
London | ||
London | 0.035 | 0.012 |
Outer London | 0.040 | 0.001 |
Inner London | 0.041 | 0.050 |
Other major cities | ||
Birmingham | 0.064 | 0.280 |
Manchester | 0.381 | 0.665 |
Glasgow | 0.002 | 0.114 |
Newcastle | 0.005 | 0.613 |
Liverpool | 0.873 | 0.672 |
Leeds | 0.043 | 0.643 |
Bristol | 0.338 | 0.995 |
Belfast | 0.077 | 0.835 |
Nottingham | 0.068 | 0.373 |
Edinburgh | 0.034 | 0.575 |
Inner London Boroughs | |
---|---|
Super Prime | Kensington and Chelsea |
Westminster | |
Camden | |
City of London | |
Hammersmith and Fulham | |
Prime Tier 1 | Islington |
Wandsworth | |
Hackney | |
Lambeth | |
Prime Tier 1 | Southwark |
Tower Hamlets | |
Lewisham | |
Greenwich |