Linear causality results.
The performance of the housing market is currently considered a measure of economic activity. This research explores the connectedness vs. the ripple effect hypothesis in the current house pricing literature. Using linear causality and nonlinear causality tests we show significant bidirectional dependence between the London house prices and other UK regions’ house prices except for Northern Ireland and Wales in contrast to the existing literature where more evidence of ripple effect is reported. Furthermore, linear and non-linear forecasting tests back these results. This result has important implications for policymakers and investors.
- House Prices
- Ripple Effect
The housing market is closely associated with consumer spending, implying that an increase in house prices boosts homeowners’ confidence. Similarly, a decline in house prices raises concerns for the homeowners due to the risk of losing the value of their property resulting in a reduction in spending and holding off personal investments. Thus, house prices have become an indicator of the economic performance of a country [1, 2]. Gallin  and Costello et al.  further show the importance of the role of housing in the economy and the effects of the underlying economic factors on house prices.
Transmission of regional housing prices within one single country has been researched widely over the years [5, 6, 7, 8, 9, 10, 11]. Regarding the UK, most of the literature focuses on the ripple effect – i.e. house prices initially originate from London and the South East and are then transmitted to the rest of the country [5, 9].1 This implies that the housing market in London is the main transmitter of shocks, but developments in other regions have no impact on London. Geographical proximity to London appears to be a decisive factor in relation to the ripple effect . Holly et al.  and Cook and Watson  report that it takes more time for a shock in the housing market of London to propagate another UK region when this region is relatively distant from London. Further according to Holly et al.  any other UK region may have an impact on London prices; however, this impact is relatively short-term.
Connectedness is defined as the inter-linkage or dependence between two or more-time series . The key differences between connectedness and ripple effect relate to implications in terms of Granger causality. Ripple effect only shows unidirectional shock transmission whereas Connecteness implies bidirectional Granger causality among the underlying variables. Zhu et al.  show that rising connectedness may be due to the information spillover considering investment aspects of the housing market which may come from geographically adjacent or economically linked regions. Our study contributes to the literature by empirically investigating the
This chapter studies the price transmission mechanism driving the UK regional house prices using linear causality and the nonlinear Granger causality model proposed by Hiemstra and Jones , and the impulse response. Application of the non-linear causality test and impulse response on the UK housing market makes this study unique in the literature. Linear and non-linear forecasting tests are further conducted as a robustness check. This chapter, thus investigates the
Our results show bidirectional dependence between the London house prices and other regions’ prices except for Northern Ireland and Wales. Thus, we provide evidence of connectedness among the house prices in London and other regions of the UK. This result is confirmed by linear causality, the nonlinear causality and impulse response tests. Further empirical examination applying linear and non-linear forecasting tests back the linear and non-linear causality results.
The format of the chapter is the following. Section 2 describes the data and the empirical methodology employed. Section 3 discusses the results, and Section 4 presents the conclusion and implications.
2. Data description and methodology
This study is based on UK regional housing quarterly prices’ data ranging from Q4–1973 to Q2–2018 obtained from the Nationwide website2 for 13 regions; these are London, East Anglia, East Midlands, North, North West, Northern Ireland, Outer Metropolitan, Outer South East, Scotland, South East, South West, Wales, West Midlands, and Yorkshire and Humberside. The different regions of the UK exhibit certain and unique characteristics. Northern Ireland is unique in the sense it has achieved an increased level of independence from the UK government since the late 1990s when it comes to social security provisions and the taxation of its housing market . Further there is a strong link between the housing markets of the Northern Ireland and the Republic of Ireland . Similarly Wales also achieved increased level of independence from the UK government after the 1997 devolution. East Midlands is a region with a very strong manufacturing in the country and is considered important when it comes to the production sector of the economy . In contrast the West Midlands has a relatively poor economic conditions . According to ONS , the South West is one of the UK regions with the highest rates of employment and economic activity. Given the uniqueness, strength and location relative to London of these other regions, it is possible for house prices in these regions to impact London house prices. Figure 1 shows the approximate location of the 13 regions relative to London. Figure 2 presents all the prices normalised to one at the start, including the UK. The close movements of all the indices are clearly visible. The rising prices across all regions during the mid-1980s and falling prices during the financial crisis of the late 2000s are clearly prominent.3
This figure shows the regional house prices of the UK normalised to one at the start of the sample period; i.e. 1973Q3 – 2018Q2.
2.2 Bivariate and multivariate linear causality
In order to examine the linear relationship between various UK regional house prices with the London house prices, we consider the widely accepted vector autoregression (VAR) specification and the corresponding Granger causality test . This approach enables us to assess whether there is a causal relationship between the variables in terms of time precedence and in which direction the causality flows. This will help us to test whether there is a ripple effect or connectedness between the prices UK regional house prices. The specification of the applied bivariate VAR model can be expressed as follows:
where, in our case,
2.3 Bivariate nonlinear causality
Arrival of new information and dynamics of economic fluctuations cause changes in the security prices. Campbell et al.  describe these processes as nonlinear. Furthermore, many other researchers have highlighted the existence of nonlinear features in macroeconomic variables and models [22, 23, 24, 25, 26, 27]. Hiemstra and Jones  reported nonlinear causality in financial variables using a correlation integral based approach. Subsequent research papers have provided more evidence on nonlinear modelling of various financial variables [28, 29, 30, 31, 32, 33, 34]. Market frictions such transaction cots and information asymmetries could be associated with the nonlinear dynamics and can cause non-convergence towards the long-term equilibrium. Anderson  reports that the transaction costs in the asset pricing literature could be one of the factor for disequilibrium error. He further demonstrates that nonlinear models which consider the transaction costs often outperform the parametric models. Some of the studies have identified heterogenous investors’ beliefs as one of the sources for nonlinearities in macro-financial time series . This heterogeneity exisit mainly due to differences in investor horizonds, risk profiles  and herding behaviour . Due to the above, we study the Granger causality in using nonlinear framework.
Correlation integral based nonlinear Granger causality was introduced by Baek and Brock  and was further developed by Hiemstra and Jones . This research studies nonlinear causality between the UK regional house prices, using the Hiemstra and Jones  test statistic.
Consider two stationary time series and for t = 1,2,…… An m-length lead vector of is denoted by wheras and are lag vectors of and as shown below:
Using the Hiemstra and Jones  framework, Y does not strictly Granger cause X if:
Porbablity and maximum norm in Eq. (4) are denoted by Pr(.) and ||∙||, respectively. The conditional probability that the deviation between two arbitrary lead vectors of of m-length is less than e, while deviation between the corresponding lag vectors of and is also less then e, is shown on the left hand side of the Eq. (4). The right hand side represent the conditional probability that two arbitrary m-length lead vectors of are with a distance of e of each other, assuming that the corresponding lag vectors i.e. and are also within a distance e of each other. For all regions,
where joint probabilities are denoted as
Details on the definition and the estimator of the variance are provided in an appendix of Hiemstra and Jones .
Table 1 shows the results for linear Granger causality based on Eqs. (1) and (2). The results show that London predominantly affects the regional house prices except for Northern Ireland, Outer Metropolitan and Outer East, and Wales. Similarly, regional house prices affect London house prices in seven out of 13 regions with some of these showing a feedback effect from or connectedness to the changes in the London house prices. No evidence of price feedback is found in any direction for Northern Ireland and Wales. The Northern Ireland and Wales results may be due to the increased independence of these regions from the UK government and the far distance location from London. Scotland prices are affected by London but not vice versa. Surprisingly Outer Metropolitan and Outer East affect the London prices but not vice versa. These results confirming connectedness between the house prices may be due to geographically adjacent or economically linked regions.
|Regions||London ➔ Region||Region ➔ London|
|Yorkshire and Humberside||14.65*||33.97***|
Table 2 shows results for the nonlinear Granger causality. This test is applied to the standardised residuals obtained from the VAR models after filtering any linear dependence among the underlying variables. The null hypothesis of no nonlinear Granger causality has been rejected in most of the cases except for Northern Ireland and Wales. This shows significant evidence of nonlinear interdependence among the housing prices of London and other regions in the UK. We report bidirectional dependence between London and the other regions except for Northern Ireland and Wales. These results evince the nonlinear feedback effect or connectedness. No evidence of any causality in any direction is found between London and Wales/Northern Ireland.
|Regions||London ➔ Region||Region ➔ London|
|Yorkshire and Humberside||13.231***||13.422***|
Further evidence is presented by means of the impulse response function. Figure 3 shows the impulse response function to one-standard-deviation innovations to the housing prices originating in London and other regions, respectively. These graphs can be interpreted into two categories – i.e. i) house prices in other regions responding to the shocks to London house prices and ii) London house prices responding to the shocks occurring in other regions in the UK. Firstly, a one per cent shock to the London house prices shows an immediate impact on house prices in most of the regions within a range from 1.5–3% – e.g., East Anglia, East Midlands, West Midlands, Outer Metropolitan, Outer Southeast, South West and Yorkshire. Geographically speaking, with the exception of Yorkshire, these regions are close to London. In other regions, although the shocks are statistically significant, they are smaller in magnitude. Interestingly, in the second category, innovations that originate in regions like East Anglia, Outer Metropolitan, Outer Southeast, South West, West Midlands and Yorkshire affect the London house prices with shocks in the range of 1% to 2.5%. This shows that London remains the central focus in the overall UK housing market and any shocks occurring here transmit to most of the regions. However, local shocks in other regions also show a spillover effect on London house prices. Antonakakis et al.  also report that East Anglia, Outer South East and South West are the major transmitters of regional shocks.
The evidence of connectedness presented here implies that although London is important from the housing market perspective, other regions also transmit the shocks back to the London market. This may be due to the information spillover (investor expectations) between different regions  although this research does not explicitly test the information hypothesis. By taking into consideration the impact of the bidirectional spillover effect of price, appropriate regulations and policies for the UK housing sector should be formulated. The results further imply the importance of house prices in other regions when investing in houses in London, and vice versa.
4. Robustness checks and further empirical evidence
4.1 Linear and nonlinear forecasting regressions
This section provides additional empirical evidence and explores the nature of the relationship between London and other UK regional house prices. Therefore, it complements the results of Granger causality and serves as a useful robustness check. To this end, we initially focus on the following forecasting regression:
where yt + h refers to the changes in the London house prices, with forecast horizon, h > 0 and x represents the changes in the regional house prices. The null hypothesis of β =0 is tested here to observe the predictability of changes in the London house prices using the other regional house prices. The corresponding results for h = 1 are presented in Table 3.
|Regions||London ➔ Region||Region ➔ London|
|Adj. R2||Adj. R2|
|Yorkshire and Humberside||12.32*||0.46||17.62***||0.46|
We report that the other regional house prices are a significant short-term predictor of the changes in the London house prices in most of the cases, with the exception of Northern Ireland, Scotland and Wales. These forecasting results reaffirm and strengthen the evidence against the ‘ripple effect’ hypothesis in the literature.
We further extend the forecasting model to show more evidence of nolinear relationship between the regional house prices. For this purpose, we use smooth-transition threshold (STR) models [40, 41, 42, 43, 44]. Simple threshold model can trigger an abrupt change in the parameter values, however, STR models are capable to allow smooth transition between different regime states. Following Smooth Transition Threshold model is used:
is the transition function and is the transition variable, whereas remaining variables are as defined in Eq. (7). Based on the existing literature, we first consider the logistic form of transition function (LSTR) as shown in Eq. (9) [40, 42, 43, 44]:
Where , d and c are the smoothing, delay and transition parameters, respectively. This function is monotonically increasing in
Here, the transition function is symmetric around c. This model emplies that expansion and contraction have similar dynamics while the these vary for the middle ground . STR module can have some issues involving the smoothing parameter , therefore, we follow the literature and using variation of the transition varible is scaled in both of the models .
In this case, the transition function is symmetric around
Table 4 presents the results of the LSTR and the ESTR models testing the changes in London house prices as a predictor for changes in the regional house prices. In the LSTR model results, the estimated transition parameter
Results for the estimated ESTR models are very similar to the LSTR results. This reaffirms the significance of the regional house prices as a short-term predictor of future changes in the London house prices in a nonlinear context and complements the previously reported results under the linear and nonlinear frameworks. Thus, ESTR and LSTR results reinforce the idea that the regional house prices have a feedback effect or connectedness to the London house prices. This shows evidence against the ripple effect where a unidirectional impact of changes in the London house prices on other regions is reported.
5. Conclusion and implications
This chapter investigates the transmission mechanism driving the UK regional house prices using the linear causality model, the nonlinear Granger causality model, and the impulse response process. We employ quarterly housing prices data ranging from Q4–1973 to Q2–2018 from 13 regions from the UK. Results show bidirectional dependence between the London prices and other regions’ prices except for Northern Ireland and Wales. This result is confirmed by the linear causality, the nonlinear causality and the impulse response tests. Further empirical examination applying linear and non-linear forecasting tests support the linear and non-linear causality results. Thus, we provide that London is not always important for the other UK regions over time, as well as that London itself may also receive shocks from other regions. Impulse response shows that London remains the central focus in the overall UK housing market and any shocks occurring here transmit to most of the regions. However, local shocks in other regions also show a spill over effect on London house prices. Identification of regional disparities can help policymakers to achieve a more balanced growth across the country. These results underline the importance of establishing appropriate regulations and stabilisation policies in the housing sector of the economy. Further, the interdependence between regional housing prices might provide significant insight regarding efficient diversification of investments across mortgage-backed securities.
- Antonakakis et al.  and Cook and Watson  provide an excellent survey of the papers in literature that investigate the ripple effect in the UK housing market. Cook and Watson  also provide a good discussion of the different empirical methods applied in these papers.
- ADF test  and KPSS test  show that the changes in the house prices (first difference series) are stationary. Results for these tests are available from the authors on request.
- See Hiemstra and Jones  for further details on correlation integrals and joint probabilities.