The spatial and temporal diffusion of house prices in the UK

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Abstract

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region – London – are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.

Research highlights

► The paper provides a method for modelling spatial and temporal diffusion. ► London proves to be a dominant region for understanding house prices in the UK. ► But New York house prices are also informative about London house prices.

Introduction

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region – London – are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.

The present paper provides a relatively simple and consistent approach to modelling spatial and temporal adjustments quantitatively.1 We approach the analysis from the perspective of recent developments in the literature on panel data models with a spatial dimension that manifests itself in the form of cross sectional dependence. One of the most important forms of cross section dependence arises from contemporaneous dependence across space and this is the primary focus of the spatial econometrics literature. This spatial dependence (Whittle, 1954) approach models correlations in the cross section by relating each cross section unit to its neighbour(s). Spatial autoregressive and spatial error component models are examples of such processes. (Cliff and Ord, 1973, Anselin, 1988, Kelejian and Robinson, 1995, Kelejian and Prucha, 1999, Kelejian and Prucha, 2010, Lee, 2004). Proximity, of course, does not have to be limited to proximity in space. Other measures of distance such as economic (Conley, 1999, Pesaran et al., 2004), or social distance (Conley and Topa, 2002) could also be employed. In a regional context proximity of one region to another can depend on transport infrastructure. The ability to commute easily between two areas is likely to be a much better indication of economic inter-dependence than just physical closeness.2

Another approach to dealing with cross sectional dependence is to make use of multifactor error processes where the cross section dependence is characterized by a finite number of unobserved common factors, possibly attributable to economy-wide shocks that affect all units in the cross section, but with different intensities. With this approach the error term is a linear combination of a few common time-specific effects with heterogeneous factor loadings plus an idiosyncratic (individual-specific) error term. Pesaran (2006) has proposed an estimation method that consists of approximating the linear combinations of the unobserved factors by cross section averages of the dependent and explanatory variables and then running standard panel regressions augmented with the cross section averages. An advantage of this approach is that it yields consistent estimates even when the regressors are correlated with the factors, and the number of factors are unknown. A maximum likelihood procedure is also suggested by Bai (2009).

More recently Pesaran and Tosetti (2010) have sought to combine the insights of these two approaches and propose a panel model in which the errors are a combination of a multifactor structure and a spatial process. To achieve this a distinction is drawn between what is termed weak and strong cross section dependence. (Chudik et al., 2010b). A process is said to be cross sectionally weakly dependent at a given point in time, if its weighted average at that time converges to its expectation in quadratic mean, as the cross section dimension is increased without bounds. If this condition does not hold, then the process is said to be cross sectionally strongly dependent. The distinctive feature of strong correlation is that it is pervasive, in the sense that it remains common to all units however large the number of cross sectional units. Significantly, spatial dependence typically entertained in the literature turns out to be weakly dependent in this framework. Holly et al. (2010) model house prices at the level of US States where there is evidence of significant spatial dependence even when the strong form of cross sectional dependence has been swept up by the use of cross sectional averages. If we were to extend the sample by including regions or countries in Europe we would still expect that the spatial effects of New York State would be confined to its neighbouring states and not extend to Europe. By contrast common factors coming from the aggregate US economy could still have pervasive effects for regions of Europe.3

As compared to purely spatial or purely factor models analysed in the literature, the spatio-temporal model estimated in this paper uses London house prices as the common factor and then models the remaining dependencies (contemporaneously or with a lag) conditional on London house prices. This allows us to consistently estimate separate conditional error correcting models for the different regions in the UK, which we then combine with a model for London to solve for a full set of spatio-temporal impulse response functions. Two alternative specifications are considered for London house prices, one specification that only depends on lagged London and neighbouring house price changes, and another which also depends on New York house prices.

While we are able to demonstrate that London is a dominant region for the rest of the UK, it is not immediately obvious why it should be uniquely so. One possibility we consider is that London is the largest city in Europe but more significantly is a major world financial centre. Developments in world financial markets can impact directly on the London housing market. Because London’s traditional role as a financial and trading centre and the attraction that it has for economic migration of highly skilled workers, residential prices reflect both local factors in the UK but also movements abroad. In particular, there is a well established international market in residential property in which London along with New York plays a role. Our test results clearly show that New York house prices are significant drivers of house prices in the UK, but only through London. We also explored the possibility that Paris house prices could be one of the drivers of London house prices but found little evidence in its support.

It is important to note that the focus of our analysis differs from many others where the intention is to understand what determines regional house prices in terms of income, housing costs and other fixed factors to explain differences in regional house prices.4 Although our approach does not preclude the inclusion of observable covariates such as incomes and interest rates we have focussed on the dispersion of house price shocks, conditioning on a dominant region (London) and neighbourhood effects, so the formulation is particularly parsimonious. It can be seen as a first step towards a more structural understanding of the inter-play of house price diffusion and the evolution of the real economy nationally and regionally.5

There is also a question of the role of the supply side. Clearly, if the price elasticity of housing supply differed markedly across regions, then responses to both region specific and national demand shocks could generate very different house price dynamics (Glaeser and Gyourko, 2005, Glaeser et al., 2008). It is generally agreed that the supply of housing is very inelastic in the UK, at least over the short to medium term. A recent study of the factors responsible for a very inelastic supply (Barker, 2004) reports that real house prices in the UK rose on average 2.4% over the 30 years to 2004. Over the same period real GDP rose by an average of 2.2%. Barker summarises a variety of studies. The price elasticity of supply in the UK is no more than 0.5 compared to an elasticity of 1.4 for the US. (see Swank et al., 2002). Indeed there is more recent evidence to suggest that the elasticity has declined to almost zero since 1990 across many regions in England (Meen, 2005).

There have been a number of other studies that have considered the spatial diffusion of house prices. One of the first was Can (1990). She studied what she calls ‘neighbourhood dynamics’ by using a hedonic model of house prices where the price of a house depends on a series of characteristics, and incorporates both spatial spill-over effects and spatial parametric drift. More recently Fingleton (2008) has developed a GMM estimator for a spatial house price model with spatial moving average errors. However, both of these studies confine themselves to the cross section dimension and do not consider the adjustment of prices over time. Studies of house prices that do consider both dimensions are van Dijk et al., 2010, Holly et al., 2010. These studies develop a model that allows for stochastic trends, cointegration, cross-equation correlations and the latent-class clustering of regions. Dijk et al. apply their model to regional house prices in the Netherlands. They pick up a ‘ripple’ effect, by which shocks in one region are propagated to other regions. Holly et al. consider the evolution of real house prices and real disposable incomes across the 48 US states and after allowing for unobserved common factors find statistically significant evidence of autoregressive spatial effects in the residuals of the cointegrating relations. Chudik and Pesaran (2010a) show that significant improvements in fit is achieved if Holly et al.’s regressions are augmented with spatially weighted cross sectional averages.

Conventional impulse response analysis traces out the effect of a shock over time. However, with a spatial dimension as well, dependence is both temporal and spatial (Whittle, 1954). Our results suggest that the effects of a shock decay more slowly along the geographical dimension as compared to the decay along the time dimension. For example, the effects of a shock to London on itself, die away and are largely dissipated after two years. By contrast the effects of the same shock on other regions takes much longer to dissipate, the further the region is from London. This finding is in line with other empirical evidence on the rate of spatial as compared to temporal decay discussed in Whittle (1956), giving the examples from variations of crop yields across agricultural plots, flood height and responses from population samples.

The rest of the paper is set out as follows: In Section 2, we propose a model of house price diffusion where we distinguish between the dominant and the non-dominant regions. In Section 3, we show how the individual models of regional house prices that have been treated separately for estimation purposes can be brought together and used for impulse response analysis along the time as well as the spatial dimensions. We also consider an extension of the basic model to allow for the effects of external shocks in the form of New York house prices. In Section 4, we report some empirical results using quarterly regional real house price data for the UK over the period 1974q1–2008q2. Finally, in Section 5, we draw some conclusions.

Section snippets

A price diffusion model

Suppose we are interested in the diffusion of (log) prices, pit, over time and regions indexed by t = 1, 2, …, T and i = 0, 1, …, N and we have an a priori reason to believe that one of the regions, say region 0, is dominant in the sense that shocks to it propagate to other regions simultaneously and over time, whilst shocks to the remaining regions has little immediate impact on region 0 – although we do not rule out lagged effects of shocks from regions i = 1, 2, …, N onto region 0. This is an

Spatio-temporal impulse response functions

Although the regional price model can be de-coupled for estimation purposes, for simulation and forecasting the model represents a system of equations that needs to be solved simultaneously. We begin by writing the system of equations in (2.1), (2.2) asΔpt=a+Hpt-1+(A1+G1)Δpt-1+C0Δpt+εt,where pt = (p0t, p1t, …, pNt), a = (a0, a1, …, aN), εt =  (ε0t, ε1t, …, εNt),H=ϕ0s000-ϕ10ϕ1s+ϕ10000-ϕN-1,00ϕN-1,s+ϕN-1,00-ϕN000ϕNs+ϕN0-ϕ0ss0ϕ1ss1ϕN-1,ssN-1ϕNssNA1=a010000a1100000aN-1,10000aN1,G1=

Regions and their connections

We apply the methodology described above to regional house prices (deflated by the general price level) in the UK using the quarterly, quality adjusted10 house price series collected by the Nationwide Building Society.11 The panel data set covers quarterly

Conclusions

This paper suggests a novel way to model the spatial and temporal dispersion of shocks in non-stationary dynamic systems. Using UK regional house prices we establish that London is a dominant region in the sense of Pesaran and Chudik (2010) and moreover that it is long-run forcing in the sense of Granger and Lin (1995). House prices within each region respond directly to a shock to London and in turn the shock is amplified both by the internal dynamics of each region and by interactions with

Acknowledgments

We are grateful to Stuart Rosenthal (Editor) and two anonymous referees, Peter Burridge, Alex Chudik, Chris Rogers, Ron Smith, Elisa Tosetti, and participants in the Cambridge Finance Workshop, the Conference on Factor Models in Economics and Finance at the Cass Business School, and the York DERS Workshop for helpful comments where a preliminary version of this paper was first presented.

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