# U.K. House Prices: Bubbles or Market Efficiency? Evidence from Regional Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methods and Materials

#### 3.1. Basic Modelling of House Price Growth

#### 3.2. Data Sources and Sample

## 4. Results

#### 4.1. Panel Unit Root Test

#### 4.2. Cointegration Test

#### 4.3. Test Results

#### 4.4. Financial Crisis Test

## 5. Discussion

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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1 | We use the cubic spline interpolation method of plugging the quarterly values for the monthly time intervals. |

2 | |

3 | We use the econometric code package “ipshin”, which estimates the t-test for unit roots in heterogeneous panels developed by Im, Pesaran, and Shin (Im et al. 2003). |

4 | We use the econometric code package “hadrilm” performs a test for stationarity in heterogeneous panel data (Hadri 2000). |

**Figure 1.**Monthly rent to price ratio, 2005–2017, U.K. Office for National Statistics (ONS), United Kingdom.

**Figure 2.**Monthly 10-year U.K. government real bond rate, Bloomberg; and U.K. variable real mortgage, Nationwide.

**Figure 4.**Montly HPI index for the United Kingdom, January 2005–December 2017, (2005 = 100). ONS, UK.

Variables | Individual ADF Based Tests | IPS Test | Hadri Test |
---|---|---|---|

Rent to Price Ratio | −1.323 | −1.452 | 18.610 *** |

Δ Rent to Price Ratio | −4.252 *** | −4.097 *** | −0.376 |

10-Year Government real bond rate | 15.137 *** | ||

Δ 10-Year Government real bond rate | −2.019 | ||

Residential Mortgage Rate | 6.705 *** | ||

Δ Residential Mortgage Rate | −0.831 | ||

First time buyer affordability Rate | −1.069 | −1.316 | 30.413 *** |

Δ First time buyer affordability Rate | −4.512 *** | −4.208 *** | −1.201 |

Disposable Household Income | −2.501 * | −1.869 * | 9.123 *** |

Δ Disposable Household Income | −4.179 *** | −4.057 *** | 7.150 *** |

Earnings ratio | −0.860 | −0.833 | 27.699 *** |

Δ Earnings ratio | −4.397 *** | −4.135 *** | 0.955 |

${\mathit{G}}_{\mathit{\tau}}$ | ${\mathit{G}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\tau}}$ | ${\mathit{P}}_{\mathit{\alpha}}$ | |
---|---|---|---|---|

R/P and 10-Year Government real bond rate | −2.187 | −7.697 | −6.896 | −8.090 |

R/P and Residential Mortgage Rate | −2.786 * | −11.761 | −7.609 * | −10.472 |

R/P and First time buyer affordability Rate | −1.142 | −2.966 | −3.181 | −2.159 |

R/P and Disposable Household Income | −1.760 | −5.102 | −4.145 | −3.837 |

R/P and Earnings ratio | −3.101 *** | −21.556 *** | −9.109 *** | −19.898 *** |

Variable | Dependent Variable: Rent to Price Ratio | |||
---|---|---|---|---|

Model A1 | Model A2 | Model B1 | Model B2 | |

PMG | MG | PMG | MG | |

Long-Run Equation | ||||

Residential Mortgage Rate | 3.712 *** (10.265) | −0.910 (−0.083) | 5.800 *** (7.226) | 1.831 (0.223) |

Earnings Ratio | −25.882 *** (−22.937) | −18.678 (−0.475) | −25.828 *** (−16.894) | −20.898 (−0.927) |

10-Year Government real bond rate | −2.388 *** (−3.931) | −0.196 (−0.054) | ||

Short-Run Equation | ||||

Error-correction (EC) | −0.079 *** (−5.560) | −0.007 (−1.046) | −0.054 *** (−5.451) | 0.013 (1.658) |

Δ Rent to Price Ratio_{t−1} | 0.938 *** (28.668) | 0.990 *** (96.368) | 0.877 *** (27.735) | 1.005 *** (123.896) |

Δ Rent to Price Ratio_{t−2} | 0.054 (1.675) | −0.310 *** (−51.879) | 0.122 *** (3.888) | −0.315 *** (−45.312) |

Δ Residential Mortgage Rate_{t} | −1.264 *** (−4.818) | −1.572 *** (−9.370) | −1.281 *** (−6.851) | −2.068 *** (−11.341) |

Δ Residential Mortgage Rate_{t−1} | 0.843 * (2.083) | 0.339 (1.003) | 0.286 (0.537) | 1.538 *** (4.153) |

Δ Residential Mortgage Rate_{t−2} | 0.817 * (2.477) | 0.218 (0.625) | −0.097 (−0.194) | −0.684 (−1.791) |

Δ Residential Mortgage Rate_{t−3} | −0.359 (−1.823) | −0.102 (−0.954) | 0.115 (0.736) | 0.14 (1.203) |

Δ Earnings ratio_{t} | −3.709 *** (−4.829) | −7.650 *** (−7.605) | −5.783 *** (−4.713) | −6.117 *** (−7.366) |

Δ Earnings ratio_{t−1} | −1.689 (−1.292) | 10.052 *** (5.935) | 7.422 *** (4.176) | 8.953 *** (6.873) |

Δ Earnings ratio_{t−2} | 5.352 *** (6.911) | −4.685 *** (−7.068) | −3.711 *** (−4.058) | −4.129 *** (−7.762) |

Δ 10-Year Government real bond rate_{t} | −0.473 *** (−4.894) | −0.282 *** (−3.385) | ||

Δ 10-Year Government real bond rate_{t−1} | 1.264 *** (7.137) | 1.041 *** (7.202) | ||

Δ 10-Year Government real bond rate_{t−2} | −0.878 *** (−6.645) | −0.844 *** (−8.199) | ||

Δ 10-Year Government real bond rate_{t−3} | 0.207 *** (4.656) | 0.217 *** (8.180) | ||

Constant | 0.007 (1.329) | 0.032 ** (2.663) | 0.097 *** (5.574) | −0.012 (−0.899) |

Observations | 1422 | 1404 | 1404 | 1404 |

Selected Model | ARDL(2,3,2) | ARDL(2,3,2,3) chi2(2) = −5.89 | ||

Hausman test | chi2(2) = −13.02 |

Region | Error Correction | ΔR/P | Δ Residential Mortgage Rate | Δ Earnings Ratio | Δ 10 Year Government Real Bond Rate | Constant |
---|---|---|---|---|---|---|

East | −0.095 | 0.064 | −0.739 | −1.957 | 0.171 | 0.179 |

East Midlands | −0.071 | 0.134 | −0.367 | −3.082 | 0.038 | 0.128 |

London | −0.002 | 0.918 | −1.565 | −1.950 | 0.084 | 0.003 |

North East | −0.087 | −0.083 | −0.861 | −1.072 | 0.282 | 0.145 |

North West | −0.060 | 0.083 | −1.539 | −0.846 | 0.082 | 0.099 |

South East | −0.027 | 0.340 | −0.598 | −3.200 | 0.031 | 0.053 |

South West | −0.041 | 0.102 | −1.687 | −2.556 | −0.069 | 0.086 |

West Midlands | −0.059 | 0.167 | −0.979 | −0.364 | 0.031 | 0.108 |

Yorkshire and The Humber | −0.041 | 0.007 | −0.466 | −3.630 | 0.430 | 0.069 |

Maximum | −0.002 (London) | 0.918 (London) | −0.367 (East Midlands) | −0.364 (West Midlands) | 0.171 (East) | 0.179 (East) |

Minimum | −0.095 (East) | −0.083 (North East) | −1.687 (South West) | −3.630 (Yorkshire and The Humber) | −0.069 (South West) | 0.003 (London) |

Variable | Dependent Variable: Rent to Price Ratio | |
---|---|---|

Coefficients | Standard Errors | |

Long-Run Equation | ||

Residential Mortgage Rate | 5.708 *** | 0.777 |

Earnings Ratio | −26.526 *** | 1.669 |

10-Year Government real bond rate | −2.190 *** | 0.616 |

CRISIS | 0.004 *** | 0.001 |

Short-Run Equation | ||

EC | −0.058 *** | 0.010 |

CRISIS | −0.036 *** | 0.006 |

Δ Rent to Price Ratio_{t−1} | −0.101 *** | 0.027 |

Δ Rent to Price Ratio_{t−2} | 0.164 *** | 0.027 |

Δ Residential Mortgage Rate_{t} | −1.245 *** | 0.204 |

Δ Residential Mortgage Rate_{t−1} | 0.221 *** | 0.563 |

Δ Residential Mortgage Rate_{t−2} | −0.045 *** | 0.530 |

Δ Residential Mortgage Rate_{t−3} | 0.099 *** | 0.169 |

Δ Earnings ratio_{t} | −5.247 *** | 1.275 |

Δ Earnings ratio_{t−1} | 6.842 *** | 1.756 |

Δ Earnings ratio_{t−2} | −3.476 *** | 0.881 |

Δ 10-Year Government real bond rate_{t} | −0.452 *** | 0.109 |

Δ 10-Year Government real bond rate_{t−1} | 1.243 *** | 0.177 |

Δ 10-Year Government real bond rate_{t−2} | −0.871 *** | 0.135 |

Δ 10-Year Government real bond rate_{t−3} | 0.207 *** | 0.045 |

Constant | 0.106 *** | 0.018 |

Observations | 1404 |

Variable | Dependent Variable: Rent to Price Ratio | ||
---|---|---|---|

Pre-Financial Crisis | Financial Crisis | Post-Financial Crisis | |

Long-Run Equation | |||

Residential Mortgage Rate | 3.6212 (5.012) | 2.481 *** (7.190) | −10.330 *** (3.450) |

Earnings Ratio | −16.493 ** (2.241) | −19.076 *** (−16.963) | −26.824 *** (4.940) |

10-Year Government real bond rate | −1.5992 (2.620) | −1.785 *** (−7.160) | 0.744 ** (0.288) |

Short-Run Equation | |||

EC | 0.013 (0.083) | −0.276 *** (−11.353) | −0.184 *** (0.033) |

Δ Rent to Price Ratio_{t−1} | 0.034 (0.543) | −0.048 (0.048) | −0.214 *** (−5.510) |

Δ Rent to Price Ratio_{t−2} | 0.037 (0.597) | 0.241 *** (0.048) | 0.012 (0.331) |

Δ Residential Mortgage Rate_{t} | −0.323 (−0.555) | −2.620 *** (−6.679) | 0.961 (1.750) |

Δ Residential Mortgage Rate_{t−1} | 0.986 (1.694) | 2.848 *** (3.541) | 0.446 (0.730) |

Δ Residential Mortgage Rate_{t−2} | 1.490 * (2.222) | −2.137 ** (-2.621) | 1.755 ** (2.790) |

Δ Residential Mortgage Rate_{t−3} | −2.374 *** (−3.553) | 0.752 ** (2.667) | −0.233 (−0.395) |

Δ Earnings ratio_{t} | −5.112 ** (−2.837) | 5.323 (1.930) | −3.232 * (−2.421) |

Δ Earnings ratio_{t−1} | 5.041 * (2.386) | −5.291 (−1.821) | −0.355 (−0.209) |

Δ Earnings ratio_{t−2} | −6.712 *** (−3.648) | 2.585 * (1.967) | −4.319 ** (−3.223) |

Δ 10-Year Government real bond rate_{t} | 0.563 * (2.292) | 0.880 ** (3.265) | 0.204 (1.752) |

Δ 10-Year Government real bond rate_{t−1} | −0.863 *** (−3.451) | −0.593 (−1.385) | −0.002 (−0.015) |

Δ 10-Year Government real bond rate_{t−2} | 0.285 (1.225) | 0.284 (0.876) | −0.447 *** (−3.926) |

Δ 10-Year Government real bond rate_{t−3} | −1.121 *** (−4.408) | −0.063 (−0.756) | −0.375 *** (−3.352) |

Constant | −0.003 *** (−5.039) | 0.480 *** (11.263) | −0.002 *** (−4.238) |

Observations | 243 | 441 | 684 |

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.; Lux, N. U.K. House Prices: Bubbles or Market Efficiency? Evidence from Regional Analysis. *J. Risk Financial Manag.* **2018**, *11*, 54.
https://doi.org/10.3390/jrfm11030054

**AMA Style**

Wu Y, Lux N. U.K. House Prices: Bubbles or Market Efficiency? Evidence from Regional Analysis. *Journal of Risk and Financial Management*. 2018; 11(3):54.
https://doi.org/10.3390/jrfm11030054

**Chicago/Turabian Style**

Wu, Yi, and Nicole Lux. 2018. "U.K. House Prices: Bubbles or Market Efficiency? Evidence from Regional Analysis" *Journal of Risk and Financial Management* 11, no. 3: 54.
https://doi.org/10.3390/jrfm11030054