In recent years, analysis and determination of house prices have been in particular interest not only to economists but also to econometricians. Changes in prices of real estate and any issues related with the house market have been also frequently discussed in the media due to the raising interest among the general population.
In the beginning of the eighties extensive financial deregulations raised the accessibility of mortgage finance and stimulated the housing demand. Banks in the UK started to profit more and more from mortgage lending. In order to continue the profitable campaign many banks became careless, lowering their criteria on house loans. At some point many bank strategies were based on the idea of massive lending without thinking of the consequences. The temporal economic stability and house market growth were misleading and it was a matter of time before people faced difficulties paying back their mortgage payments. The increased number of the so called "bad loans" led the banks into trouble. They started facing liquidity problems and the first big victim was Northern Rock  . UK's biggest provider of mortgage loans collapsed and soon after that, the whole economy was already facing a recession. It took nearly three years for the UK to exit the recession and the result was only a 0.1 per cent GDP growth for the last quarter of 2009. What this paper wants to focus on is the house price behaviour in the pre-crisis period in the UK.
Many OECD countries like UK, USA and Spain experienced a more than 70 per cent increase in house prices for the period between 1996 and 2005. By historical standards, this was a strong performance. The real estate sector played a big and important role in the recent global recession and many concerns were raised about overvaluation of house prices. In general, houses act as any other good being traded on the market and they should be highly sensitive to the surrounding economic environment. Moreover, the high increase of dwelling values in the period of discussion must be supported and explained by economic fundamentals. A lack of econometric evidence for the movements of house prices might suggest an existence of a "bubble"  in the housing market.
In this paper I use monthly time-series data for a ten year period raging from 1996 to 2005 to analyse the performance of the UK house market. I employ co-integration analysis and Vector error-correction model approach to assess the long-run equilibrium and the short-run dynamic of house price movements in respect to several macroeconomic fundamentals.
The exposition of this paper is organized as follows. The following section surveys previous theoretical and empirical literature on house price behaviour. Section 3 derives the model in the paper and explains the choice of variables. Section 4 applies the Vector-error correction model and presents the results obtained. Finally, section 5 concludes.
2. Brief economic background theory and literature review
House price dynamics is a widely discussed topic and there is a variety of studies based on it. The number of academic papers has tripled since the beginning of the rapid increase in house prices in industrial countries in the late nineties. The most popular areas of research are forecasting house prices, testing for existence of speculative bubbles and testing for house market efficiency. According to the existing literature on the topic, the analysis could be divided into two major approaches. The first approach is more related to macroeconomic theory and tries to explain house price behaviour with the surrounding economic environment. The second approach shares ideas from the financial literature by examining the price-rent ratio similar to the price-dividend ratio. This approach applies present value models and Campbell, Davis, Gallin, Martin (2009) suggest that: "understanding the underlying structural links between housing and financial markets is likely to be a fruitful area of future research". The discussion in this section will be divided into two parts. Firstly I will discuss briefly literature based on global house market behaviour. In addition, the close economic and social behaviour in US and UK tend to reflect the nature of the housing market in the two countries and therefore the paper will mention some of the main contribution papers on the US property market. Finally, the rest of the section will concentrate only on the UK house market.
2.1The global and US house market.
Many papers on house price behaviour present more general approaches and try to explain the global movement of house markets with the help of panel data models. McQiunn and O'Reilly( ) use panel data analysis and propose a theoretical model where the behaviour of house prices is explained by changes in real personal income and interest rates. They apply panel econometric approaches and singly country approaches for 16 OECD countries for the period between 1980 and 2005. Using co-integration analysis their results support the existence of a long-run relationship between house prices and the fundamental factors. The study also found significant short-run coefficients of adjustment and reversion to fundamentals.
Beginning with one of the early studies on house prices, Poterba (1984) develops a dynamic model for house prices and economic factors in the US housing market. The results obtained from the analysis suggest that the decrease in mortgage rates and the rising inflation in the US are the main reason for the 30 per cent increase in properties in the seventies. The paper managed to partially provide a framework of the equilibrium but issues such as risk in investment and tax treatment were ignored. Case and Shiller (1989) are some of the pioneer works on the topic of house prices. Their work was based on time-series regional analysis of the US house market efficiency. The paper suggests that there is a significant persistency in changes in house prices. In addition, the results state that forecasting citywide indexes tend to be highly influenced by noise  . However, the paper fails to measure the return on housing accurately, based on the difference in quality in rent indexes. Moreover, any attempts to explain any tax effect runs into difficulties and some of their finding could not be applied in several regions in US. Case and Shiller (1989) has a significant contribution to the early studies of the topic and has been cited by many research papers.
In more recent studies of the real estate market in US, Mikhed and Zemcik (2009) investigate whether the rapidly increasing prices of houses prior to 2006 could be justified by several economic factors such as building costs, stock market wealth, mortgage rate, personal income, rent and population. The paper employs co-integration analysis for both regional and aggregate data and based on their results they conclude that there was a house price bubble in the US in the period between 1995 and 2006. In addition, univariate time-series tests for individual Metropolitan Statistical Areas point out that the burst of the bubble which occurred after 2006 has not still put prices in line with their fundamentals and house price might drop even more. The period from the late nineties to the beginning of the Global Recession is very sensitive and there are many contradictions among econometric studies. Several more papers support the existence of a bubble. Shiller (2005) and Gallin (2006) both came to conclusion using aggregate data that the fast growth in US house prices is not explained by shifts in fundamentals after 2000. However, McCarthy and Peach (2004) managed to estimate a model which results came to opposite conclusions that there was no bubble in that period in the US and that the changes in house prices reflect movements in nominal mortgage rate and personal income. In addition, Smith and Smith (2006) results stated that house prices were even below fundamentals, which were derived from house rents where prices and rents were taken from a sample of matched single-family homes.
As mentioned above in the section, financial market models were applied on house prices in existing literature. As an example Clark (1994) paper investigates whether movement in house prices and rents in the US market are dependable on the forward-looking behaviour of the present value model. According to the model in areas where the price-to-rent is high, the future rent growth will be slow. His estimates back up the hypothesis and state that present value model tend to be important in house price valuation.
Caliman (2009) discussed the Italian housing market in the period from 1995 to 2003 and its exposure to busts. The paper used GMM method of estimation for house prices in different provinces  in Italy. The results came to the conclusion that in Italy house prices are largely justified by economic fundamentals. Moreover, according to the findings the constant increase in rents and the drop in mortgage rates explain most of the increase in house prices. In addition, the paper provides a forecast of future movements in prices and it suggests that any unexpected drops in prices are very unlikely. With similar intentions but different approach Merikas, Triantafyllou and Merika (2009) use co-integration approach for their study of house prices and economic factors in the Greek house market. They use quarterly data for the period from 1985 to 2008 and their finding suggest that the main fundamental factor explaining house price volatility are inflation, interest rates, unemployment and stock market. However they mention that a big part of the shifts in prices is caused by: "behavioral factors inherent in the Greek society".
Another Mediterranean country experienced a significant house price appreciation in the period starting from the late nineties up to 2003. In their paper Ayuso and Restoy (2006) they employ GMM and VAR models to measure the overvaluation of the market in relation to rents. Their main findings were that the price-to-rent ration in 2003 was above equilibrium in all three countries. In addition, their results showed that UK was about 30% in disequilibrium, Spain around 20%, and 10% for the US. They stated that most of the disequilibria in Spain and UK can be explained by the slow adjustment of rents and also to the lack of quality house supply.
The UK house market
Hasan and Taghavi (2002) aim was to examine the relationship between macroeconomic variables and residential investment over the period 1968-1999. In their paper they use a co-integrated vector autoregressive model for six variables- output, mortgage rate, residential investment, money supply, government spending and price. According to their results in the long-run fiscal policy has a modest effect on residential investment, whereas monetary policy appears to have larger and noticeable impact. The papers findings confirm that the house price inflation has seriously increased after the monetary deregulations in the 1980s.
An important point in our discussion on house markets is the wealth effect from increased prices of property. People tend to increase their consumption when the price of their house increases. In the mid nineties the residential property in the UK was around 35 per cent of the average household wealth (The National Bureau of Economic Research, 2009). As we can see the residential property of household plays a big role in the behaviour of people and their consumption. Moreover, the housing wealth effect may be especially important in recent decades, as institutional innovations (such as second mortgages in the form of secured lines of credit) have made it as simple to extract cash from housing equity. Furthermore, from the homeowner point of view it makes sense to use a mortgage to fund spending because mortgage interest rates are typically considerably less than those on credit cards and unsecured consumer debt. In fact, economic papers like Case and Shiller (2001) have observed that wealth effect associated with real estate are more significant that those linked to financial asset holdings in most economies. In their work they use both time-series and cross-sectional data to estimate the effect of house price movements and stock market movements on the consumption. According to their results a 10 per cent change in house wealth is related with roughly 1.1 per cent increase in consumption. The results are from international panel data, which includes developed countries for the period between 1980 and 1999. In addition, the same 10 per cent increase in stock market wealth has virtually no effect upon consumption. All of their empirical results support the conclusion that changes in house prices have a larger and more important impact than changes in stock prices on household consumption in US and other well-developed countries.
. Gallin (2004) showed that when house prices are high relative to rents changes in prices will be smaller than usual and changes in rents will be larger than usual. He used long-horizontal regression approach to prove that the rent-price ratio helps prediction of future changes in the housing market. The results lend empirical support to the view that the rent-price ratio is an indicator of valuation in the housing market. Moreover, Leamer (2002) suggests that when the rent-price ratio of housing gets too large the whole market is at disequilibrium.
Many studies try to test directly the relationship of rent-price in a manner similar to that of dividend-price ratio in the financial literature (Case and Schiller 1988, Clayton 1996). This approach uses present value models and has the advantage of not requiring the specification of user cost of housing or market price of house services. However, Badev (2006) argues that one of the drawbacks of this approach is that the relationship between prices and rents is typically affected by supply restrictions, regulations and contractual practices that are not easily captured by the standard asset financial models.
In their recent work Campbell, Davis, Gallin and Martin (2009) find a number of interesting similarities between house markets and financial markets, although they are both quite different in both form and function. According to their paper the understanding of structural links between housing and financial markets is likely to be "a fruitful area of future research". In their study they use the applications of the dynamic Gordon growth model to the housing market. Moreover, the paper provides an insight into the fundamental sources of variability in housing valuations. Aside from providing direct evidence on the nature of fluctuations in rent-price ratio, the framework they adopt allows for a meaningful comparison of housing and other financial assets. The model used in their work splits the rent-price ratio into the expected present discounted values of rent growth, real interest rates, and a housing premium over real rates. They show that housing premiums are variable and forecastable and account for a significant fraction of the rent-price ratio volatility at national and local levels for the US, and that covariances among the three components damp fluctuations in rent-price ratios. Thus, the explanations of house-price dynamics that focus only on interest rate movements and ignore these covariances can be misleading. The results they obtain are similar to those observed for stocks and bonds.
Badev (2006) uses three different approaches in his paper to provide evidence for the relationship between house prices and rents in the United States. The third analysis provides the most conclusive evidence that house prices correct back to rents. In his analysis he uses bootstrap procedure to construct artificial data that conform to his null hypothesis that rents and prices are cointegrated, but that rents do all the correcting. Additionally, the newly constructed artificial data is used in a long-horizontal regression analysis to examine how the rent-price ration is related to changes to real rents and prices over three-year horizons. Furthermore, expectations would suggest that rents will "correct" much faster than they do in the data. In addition, the data shows a positive correlation between the rent-price ratio and real house prices instead of what we would expect, which is a negative coefficient. These results provide evidence against the null that rents do all the correcting and that prices do none. Studies like Badev (2006) suggest that the rent-price ratio is a reasonable measure of the valuation of the market. However, the paper takes into account that it needs better measures of house prices and rents to fully understand their relationship and also that it essentially ignores potential transaction costs and the risks involved in renting and owning. Furthermore, he concludes that we cannot expect the rent-price ratio to be a precise indicator of market valuation because as any other asset price movements, house prices are notoriously hard to predict.
Study of Ayuso and Restoy (2005) uses a general inter-temporal asset pricing model where housing services and consumption are non separable to measure overvaluation of housing in relation to rents in the United States, United Kingdom and Spain. According to their paper part of the increase in real house prices during the late nineties can be seen as a return to equilibrium following some undershooting after previous price peaks. However, the results obtained from their analysis show that the increase in house prices led the rent-price ratios above market equilibrium by mid-2003. Moreover, the ratios were above equilibrium by 30 per cent in the UK, by 20 per cent in Spain and by 10 per cent in the US. It is worth mentioning, however, that part of the overvaluation, especially in Spain and the UK, may be an attribute to the sluggishness of supply in the presence of large demand shocks in this market and the slow adjustment of observed rents to the conditions prevailing in the housing market.
Not all of the research on relationship between rents and house prices share the same approach. The papers mentioned so far in this section focus on the idea of similarities between house markets and financial markets and try to get an overall idea of house price movements and rents movements using analysis and techniques used in finance. However, a class of studies, referred as sharing a macroeconomic approach, follow Potebra (1984) and ground the house price on models of supply and demand for housing whence relating it to a set of macroeconomic variables (Topel and Rosen 1988, Mankiw and Weil 1989, Muelbauer and Murphy 1997). These studies combine an asset return condition with housing services supply rule to express the equilibrium in house market as a function of surrounding economic environment. As mentioned earlier in the section, rents tend to be an important fundamental in the formulation of house prices and house market equilibrium. A good definition for house market disequilibrium is when a growth in price is not supported by fundamentals given by Stiglitz (1990). Moreover, in our case, the period between 1990 and 2006 has been related to a period characterised with the existence of a house bubble. Gallin (2006) and Mikhed and Zemcik (2007) employ panel data for the US to analyse house prices. Furthermore, they use income and rent as the only fundamental factors. Their results find that house price dynamics in the nineties cannot be explained by either of the two variables. While discussing the US market it is worth mentioning some other studies which make conclusions about market overvaluation by the support of the relationship between house prices, rents and other fundamentals. Case and Schiller (2004) were in favour of the existence of a speculative bubble in many regions of the US housing market based on the results of a survey of consumers' attitude towards housing. Moreover, Mikhed and Zemcik (2009) use a variety of macroeconomic fundamentals such as real house rent, mortgage rate, personal income, building cost, stock market wealth, and population in order to try to explain the movements of house prices. Based on the evidence they provide using univariate and panel unit root and cointergration tests, they conclude that there was a house bubble in the US prior to 2006. According to further conclusions the house price correction starting from 2006 has not been enough to return prices to fundamental and they suggest that prices may decline even further. However, not all of the studies share the same opinion. For example, Himmelberg (2005) argue that the high price-to-income and price-to-rent rations observed in that period were explained by shifts in real long-term interest rate and therefore there was no bubble in the US housing market. Moreover, Smith and Smith (2006) suggested that house prices were below their fundamental values derived from house rents where prices and rents were taken from a sample of matched single-family homes.
Looking from a prospective point of view, several research papers on the topic try to test the predictive power of the rent-price ration in order to forecast future house price movements. Gallin (2004) use a long-horizon regression approach to make forecast for future house price movements for three periods in the future. According to his results when house prices are high relative to rents (that is when the rent-price ratio is low) changes in real rent tend to be higher than usual and changes in real price tend to be smaller than usual. Furthermore, Murphy and Junhua (2009) study house price volatility through rent-price ratio predictive power across different regions in the US. They find evidence of overshooting in house prices in all of the regions they studied. Moreover, results show that there is a consistency of response to over- and under-valuation among house prices across the US, namely that price overshoot. However, for rents they found that regional differences in behaviour, with overshooting occurring in most, but not all, locations. Therefore, in our discussion we need to take into account that many models do not include factors such as transaction costs of rents, demographic factors, and other variables which exist and could also have significant effect on any kind of house price and rent volatility.
All the assumptions and approaches so far do not take into account the quality of rents and houses. Chang, Cutts and Green (2005) use hedonic regression approach and tries to find out whether or not changes in the price of houses and rents in the nineties are product of change in quality of the housing stock or explained by economic fundamentals. In their paper they support the rent-price ratio hypothesis. They conclude that a straight comparison between widely used indexes without quality-adjustment is not recommended. Moreover, it could lead to incorrect conclusion and also suggest existence of imaginary bubble. Indeed, Capozza and Seguin (1995) argue that a price-rent ratio is a "successful" predictor of the appreciation rates only after the cross-sectional differences of owner-occupied versus rental housing are taken into account.
In conclusion to our brief examination on existing literature and theory of the topic, we can say that studies on relationship between house prices and rents can be divided by two different approaches. The first approach shares the macroeconomic point of view. Moreover, house prices movements have been related to fundamental economic factors such as interest rates, real rents, economic growth etc. However, the second approach directly test an implicit relationship between house prices and rents, using present value models that resemble those used to explain the price-to-dividend ratios in the financial literature.