The last 30 years has seen the UK economy experience many economical cycles, most notably during the economic bust of the early 1990s. Many boom and bust cycles have occurred in the UK since the 1970s and have resultantly made the housing market suffer too. Therefore house prices in the UK are susceptible to fluctuations too. But which macroeconomic factors truly affect the house prices in the UK? This is the question investigated within this paper with particular significance given to the affects of income, interest rates and inflation upon house prices.
During the late 1980s there was significant growth in real estate wealth due to low interest rates, by loosening the monetary policy and due to high consumer expenditure. The economic growth during this period, known as the Lawson boom, was as a result of the government responding to the early 1980s recession which had caused the economy to suffer, which incidentally was also brought about by the conservative government. The monetary policy structural changes in the late 1980s caused the property boom during this period as a result of widespread financial liberalisation. This increased affordability as mortgage credit was readily available since borrowing constraints had been lifted and therefore heightened the demand for housing.
The financial deregulation of the late 1980s enabled the competition in the mortgage market to increase. Building societies were allowed to compete against banks and also the retail industry was welcomed into the financial services market. This increased competition resulted in the customers able to shop around for competitive rates since affordability of housing had increased. The increased competition also resulted in credit being easily available and enticing more people in to the property market. As a result, ‘real house prices rose by over 4.5% per annum during the decade' (Pain and Westaway (1997)). Muellbauer and Murphy (1997) report that this caused a consumption boom to occur. As house prices increased, households were able to finance more consumption as they could extract housing equity. This is also known as mortgage equity withdrawal.
However as these and other economic measures were taken by the government to counteract their previous actions which had caused the recession in the early 1980s. They failed to recognise and react that in their eagerness to get the economy growing again, it had almost reached boiling point as inflation was accelerating. As the inflation growth continued unsustainably, action was taken by tightening the monetary policy and so forcing the UK economy to plunge into recession once again in the early 1990s. This obviously affected the real estate market which crashed resulting in ‘house prices falling by around 7.5% between 1990 and 1992' (Pain and Westaway (1997)). The bust which was initiated due to the high interest rate, reaching 15% at its peak, lasted for a period of almost 5 years, in which the housing market suffered significantly. Repossessions of properties became common during this period as home owners found it difficult to meet their mortgage payments. As a house is the most important asset owned by households, the government needed to intervene to depress the rising repossessions and prevent households from entering into negative equity.
During the mid 1990s, the need was felt to take dramatic action and prevent another cycle of a boom followed by an economic bust. Therefore as the Labour government came into power they decided to stimulate changes in the monetary policy and announced that all monetary policy decisions would be controlled by the Bank of England. The constant monitoring of interest rates eased inflationary pressures, and directed the economy to sustainable growth in the economy. With the control of monetary policies in the hands of the bank of England, the housing market started to flourish and marked changes in house prices started to occur. With a sustained low interest rate, more first time buyers were able to enter the property market and existing home owners had lower payments towards their mortgage, whilst other homeowners refinanced.
Since the crash of the housing market in the 1990s, the housing market has been flourishing, with house prices in different regions reaching new peaks. However whilst the house prices continue to increase, the household incomes have not grown at the same rate. This can result in the market being volatile since the high house price to earnings ratio will not be maintained. This once again resulted in another boom and bust economical cycle. The financial crisis that started from 2007 till this date has inevitably affected the UK housing market. However the housing bust this time around is much different from the previous one. Firstly the length of the housing bust has been much shorter. In 2009, house prices unpredictably started to rise after a constant dip in prices since 2007. However the fall in house prices during this period affected household consumption as households have less collateral to borrow against. Therefore this financial crisis also saw a credit crunch occur. Banks and other financial institutions tightened the accessibility of mortgage loans as they are less willing to take risks since the value of collateral has reduced. But this time around the government pressurised the banks to repossess fewer properties and as a last resort. However as the economy continued to go into recession in 2009, it is possible that repossessions will not halt since unemployment rates in the UK continue to increase. The monetary policy committee during the financial crisis have tried aiding by attempting to retain a low interest rate. Therefore as the interest rates steadily declined and so fewer people should have difficulties in meeting their payments. But they are still unable to extract equity. Therefore the decline in housing and equity values puts inflationary pressures on the economy.
As a result of assessing the UK housing market over the last 30 or so years it is evident that economic factors such as inflation, interest rates and income are always involved in the housing market, but how significant are these factors towards the state of the housing market in the United Kingdom. Therefore using different models, the impact of these individual factors on the housing market will be analysed. Also the dependency of these variables on one another will also be assessed in terms of their influence on the housing market, and in particular house prices.
The rest of this paper is organised as follows. In section 2, the analysis of previous works on the different fundamental economic factors that affect the housing market is carried out. Section 3 describes the approach that is intended to be taken and the different econometric principles to be used using a model. In Section 4 the empirical results of the tests carried out on the dataset will be reported. Concluding remarks will be given in section 5.
In this section of the paper, analysis of previous theoretical literature addressed by various economists on the topic of the Housing Market will be presented. These various papers investigate the determinants of the housing market and the impact of the diverse factors on house prices. The housing market represents a large fraction of economical wealth and is a major component of each individual household's wealth. Therefore any fluctuations in the housing market can result in serious consequences for the wider economy, producing economic booms or busts. For that reason the housing market has proven to be a very volatile, and dwellings of any sort represent risky assets with unpredictable prices. The UK housing market has experienced a continual acceleration in property prices. Campbell and Cocco (2007) report that mean real house price growth for UK houses from 1953 to 1999 was 2.1%. House prices have a huge importance in the UK economy and ‘represent more than 40% of total UK household wealth' (Aoki, Proudman and Vlieghe (2004)). Therefore the various variables affecting the housing market are scrutinized in this part.
Firstly, I will address different population characteristics. Trends in demographic factors play an important role in shaping the demand for housing. Therefore, population growth has been recognised as the primary driving force for the increase in the demand for housing, and an increase in population should simultaneously increase real house prices. However an ageing population coupled with the choice of households to increase or decrease in family size plays a pivotal role in the demand for housing. Farlow (2004) agrees with this, stating that the ‘continued proportionate reduction in the number of married and cohabiting couples' has increased the demand for housing in the UK. Therefore, more individuals are living by themselves in smaller residences.
Holly and Jones (1997) also agreed with this notion and believed that the average age for a first time buyer to get on to the property market has a major effect on the real house prices. Therefore the proportion of the population between the ages of 2029 plays a significant role. It is within this age category that the majority of the population obtain their first property purchase and take their first step into the property market. These factors affect the number of households formed and the nature of accommodation selected. Consequently increasing the demand and forcing house prices to increase. Campbell and Cocco (2007) argued that an ageing population will result in ‘more young households plan[ing] to increase house size later in life... [whilst] many old households plan to move to a smaller house later in life' which would further support the increased demand for housing, and ultimately affecting real house prices. Therefore with an ageing population, a greater number of people are living for longer periods of time, whilst the population is continuing to grow with constant births occurring. Hence sooner rather than later the supply of houses will be inefficient for the persistent demand.
However, Green and Hendershott (1995) found that age was paralleled with schooling and therefore education had an impact on the ‘willingness of households to pay for a constant quality house.' In the 1980s, 70 year old households were less willing to pay for a constant quality house compared to 50 year old households by almost 50%. But this is not due to the age rather the ‘fact that 70 year olds in the 1980s had far less education and income than 50 year olds'. Therefore as they had limited education, they were limited in their skills for certain jobs, and so affect their earnings ability. For that reason they are less willing to pay for a higher quality house. They also found that marital status had an impact too. Singles are only willing to pay 80% compared to married for a constant quality house. However they concluded that an ageing population should not lower real house prices. But we learn that education and income affect the choice and quality of dwellings.
Banks, Blundell, Oldfield and Smith (2004) addressed the issue of fertility in different age households. According to them by the age of 40 the size of the family is complete and thus there is an increase in housing services and demand throughout the different age structures. Thus, as the family size is complete, the households need to increase the size of their house, supporting Campbell and Cocco (2007) and so affect the demand for housing.
According to Holly and Jones (1997) the most important and fundamental factor of house prices is real income. Their data over the last 60 years showed that house prices had increased in parallel to income. As a result they showed that since 1939, real income has risen by 312% whilst real house prices have risen by 278%. In their model they attempt to show a long run cointegrating relationship between house prices and income. Their model differed from the approach taken by Pain and Westaway (1997). They condition their approach on the demand for housing services using permanent income, whereas Pain and Westaway (1997) conditioned on consumption. Holly and Jones tested their model using the Johansen test, an error correction model and for asymmetries. They proved that income is the most important determinant of real house prices, and that house prices are asymmetrical. If house prices are above the long run equilibrium path they adjust more quickly than below the cointegrating relationship.
McQuinn and O'Reilly (2008) also believe that an increase in the level of household income will impact the demand in the housing market. They perform tests for asymmetries supporting Holly and Jones' (1997) findings that there is a long run relationship between the amounts borrowed and house prices. Their analysis focuses on the relationship between income, interest rates and the type of mortgage. The demand for housing depends on the amount that house purchasers can borrow from financial institutions, given their current disposable income and the current mortgage interest rate. It is common knowledge that higher household income will cause an increase in their consumption and thus an increase in the demand for housing and housing services. The magnitude of the shift is influenced by the income elasticity of demand. Muellbauer and Murphy (1997) find a long run income elasticity of demand for housing to be 1.32. They find that there is an increased role for income growth expectations and wealth effects since 1980s, as a result of the financial liberalisation. This made mortgage credit easily accessible by relaxing borrowing constraints. Therefore the housing wealth to income ratio grew and they found that the elasticity of house prices to income to be 2.5. According to Carliner (1973) initial thoughts were that income elasticity of housing demand was inelastic, however this is proven to be flawed later on.
Muellbauer and Murphy (1997) also carried out OLS regressions and found that interest rates are also significant at the 5% significance level. Interest rates are also found to be a determinant of the house prices. Low interest rates encourage customers to borrow from financial institutions and in theory result in higher house prices. The Bank of England sets interest rates to meet an inflation target and encourage economic growth. McQuinn and O'Reilly (2008) believe that interest rates are a principal factor of house price movements. The amount that can be borrowed by a house purchaser is dependent upon this factor and disposable income. In general higher interest rates increase monthly mortgage payments. Therefore this acts as a deterrent and dissuades buyers from entering the property market and making a purchase. Also if interest rates increase too much, some people may struggle to meet their mortgage payments. This means they will have to sell their house, or risk repossession. This affordability effect will thus reduce demand for dwellings and therefore result in lower house prices.
Farlow (2004) stated that lower nominal interest rates meant that more first time buyers were able to get on to the property ladder as well as being able to borrow a much larger amount. Homeowners are also able to take advantage of the low nominal interest rates by taking on larger debts and consuming more housing services. However Van Order and Dougherty (1991) adopt a neoclassical model to determine the effect of inflation on housing demand, and consequently found minimal evidence supporting the hypothesis that high nominal interest rates affected housing demand in the 1970s. It is possible that they found little support for their hypothesis since it is real interest rates that affect the affordability of housing and therefore borrowing is not constrained as it may seem. Conversely, Campbell and Cocco (2007) indicate that an increase in expected inflation would also increase nominal interest rates and nominal payments. This would lead to higher real mortgage payments. Barrell, Kirby and Riley (2004) support Farlow and argue that low nominal interest rates have encouraged more first time buyers into the market due to the ‘lower liquidity constraints'.
The financial deregulation of the 1980s resulted in the removal of restrictions placed on both building societies and banks. Building societies were able to compete in the wholesale funding market, whilst banks were allowed to compete in the mortgage market. Retail institutions also entered the frame and started offering financial services. This heightened competition enabled households to ‘extract equity more easily when house prices rise' for household services and consumption (Aoki, Proudman and Vlieghe (2004)). One of the tax reliefs to be lifted during the liberalisation was mortgage interest tax relief. Muellbauer and Murphy (1997) noted that there was heightened action amongst first time buyers to purchase a property before the eradication of this relief, hence causing increased house prices. Farlow (2004) noted that as a result of credit being so easily accessible ‘first time buyers borrow 2.5 times income compared to 2 times over the last 30 years.' Therefore it had driven up house prices remarkably with the ‘average house price [being] over 5 times [the] average potential first time buyer income'. Therefore mortgage repayments represented a higher percentage of income.
Due to the financial deregulation and increase in house prices, Muellbauer and Murphy (1997) believed that these factors contributed to the consumption boom in the 1980s. ‘The magnitude and volatility of housing wealth have led many to suggest that house price changes have significant effects on aggregate consumption' (Campbell and Cocco (2007)). Therefore it is important to understand the relationship between house prices and households consumption. Campbell and Cocco (2007) believe that an increase in house price does not necessarily increase wealth and thus consumption. Rather Aoki, Proudman and Vlieghe (2004) and Ortalo  Magne and Rady (2006) believe that houses can be used as collateral. Therefore increase in house prices would mean that more funds may become available using the property as a pledge to a lender. This would persuade households to take on a mortgage equity withdrawal (MEW) to finance consumption and housing investment due to the additional borrowing obtainable. Muellbauer and Murphy (1997) believe that changes in house prices enable borrowing constrained consumers to trade off borrowing opportunities between the present and the future via the collateral effect. Aoki, Proudman and Vlieghe (2004) agree that when house prices increase and thus housing equity rises, consumers have an option between current consumption or discounted future finance premium.
Campbell and Cocco (2007) found that the relationship between house prices and consumption is greater for elderly households compared to young households. They showed that older owneroccupied households increase their consumption as house prices rise, whereas young renting households reduce their consumption. Since they estimated that the house price elasticity of consumption is 1.7. Hence estimating that as the population ages, ‘consumption may become more responsive to house prices'. But those consumers with low income will remain renting and thus will continue to have lower consumption regardless of their age. Having carried out baseline regressions, they found that consumption is positively correlated with house price changes and income growth. Since a 1% increase in house prices would lead to a 1.22% increase in consumption. Supporting these results, Pain and Westaway (1997) also derived a model of house price equation using consumption rather than income and found that house prices depend upon consumption.
Aoki, Proudman and Vlieghe (2004) using a financial accelerator approach believe that the ruleofthumb households or those with low incomes would more likely remortgage to extract housing equity for financing consumption. Their model elaborated on the imperfections of the credit market and how consumption is responsive to changes in property prices. However due to the availability of unsecured credit loans there are fewer ruleofthumb consumers. Also according to them fluctuations in the external finance premium, caused by information asymmetries, affects household consumption when properties are used as collateral in loans. Therefore less borrowing constrained consumers are able to react better to monetary policy shocks and thus able to smooth consumption. However, Farlow (2004) believes that household consumption in the UK is not as dependent on house prices as thought initially.
Another possible determinant of house prices is speculation based on expected changes in future house prices. Levin and Wright (1997) believe that a speculative opportunity arises from the timing of purchase and sale contracts. A house mover who believes that house prices will rise will make a capital gain, if the mover can strike a deal and exchange contracts on the new property before settling a sale price and exchanging contracts on the existing property. The house mover will only benefit from this if they are able to forecast a growth rate correctly and subsequently provide significant increased rates of return for the house mover. They found that speculative opportunities cause buyers at any given income level to enter the property market and make a purchase. It is possible to hold 2 properties at once if conditions are in favour with this speculative mechanism. Another possible factor that caused changes in house prices is when high permanent income homeowners are motivated to enter the market and purchase larger dwellings. Muellbauer and Murphy (1997) also recognised that speculative mechanism gave opportunities to understand the relationship with house prices. However they also concluded that it is difficult to forecast an expectation since the property market is inefficient and goes through periods of instability.
To date there have been many periods of volatility in the housing market due to all different causes. Muellbauer and Murphy's (1997) paper investigates the causes of booms and busts in the UK over the last 40 years. These booms and busts have all been affected by the factors discussed above in some sort. Like the bust in the 1990s which was caused due to the high interest rates and decline in income growth. Their model implied that busts are caused due to ‘unfavourable demographic trends, high levels of debt and high after tax real interest rates'.
A factor not discussed in the articles above is the limited supply of houses which can also be a cause of either a boom or a bust. Generally speaking, the supply of new houses is limited since it takes builders a long time to overcome planning restrictions and time to carry out the build. Therefore instability in the market can cause changes in the property market. On the other hand in a boom builders are keen to make capital gain by building more houses. However Farlow (2004) states that UK house supply is small and falling. This therefore drives up prices for existing second hand houses. Recent restrictions and greater awareness by mortgage lenders and the tightening of goverment regulations during the current economic crisis has led to changes in house prices and the housing market.
After discussing all these papers it is obvious that houses prices is dependent upon many variables since a lot of the factors are interlinked. These determinants hence affect the affordability of houses due to the dependency of the demand and supply of houses in the UK.
From the previous section it is evident that interest rates, inflation and income do play a pivotal role in the outcome of the property market's volatile prices. Thus as a result it will be attempted to develop these findings and constructively scrutinize these factors with the intention of empirically supporting the hypothesis. A number of different econometric models have been used by economists to analyse the implications of the fundamental aspects of the economy that affect the house prices within the UK.
Barrell et al (2004) and A Farlow (2004) both affirm that the lifecycle model of consumption is the approach used by economists for contemporary models of house prices. It analyses the correlation of the determinants of the market over a period of time. The alternative framework is to use a reduced form equation approach. In this model a system of statistical models are reduced to form a function for the dependent variable. In the model, the precedence will be upon the examination of the impact of demandside variables on house price fluctuations. The paper argues that the demand for housing and ultimately house prices is reliant upon interest rates, inflation and income since these variables control the amount that a consumer can borrow from financial institutions in aid of purchasing a property. Thus the consumer yearns for favourable conditions regarding these variables for maximum credit.
A wide variety of econometric systems will be used to analyse the time series data. Regression analysis is one of the primary techniques, which highlights the correlation between dependant and independent variables. The relationship between the different variables will highlight the impact each independent variable plays upon the dependant variable. The superiority of each individual variable will be examined, with an extensive range of techniques at disposal. These include Simple Linear regression and Ordinary Least Square (OLS) regressions.
Quarterly data from the UK economy over the period of 1980 to 2009 was obtained to investigate the argument presented above. The quantitative information was acquired from various sources, such as the Office of National Statistics, Nationwide and DataStream sources. After collection of the data, plotted graphs will indicate the relationship between the dependent and independent variables. From these graphs, various mathematical models can be constructed in the form of:
Where, Yt will represent the average house prices in the UK,
X will represent income, inflation or interest rate
C1 is known as the intercept
M1 is known as the slope.
However as the above equation only represents a mathematical model, it is invalid in the conclusions it leads to. It assumes that there is a linear deterministic trend between the economic variables, but this is flawed. Therefore an econometric model is developed which takes into account the random error term which is concerned with other random variables affecting the Yt variable. For that reason a simple linear regression model is produced.
Where, εt corresponds to the random error term.
However since we are concerned with the relationship between house prices and three other explanatory variables, we require that average house prices is a linear function of income, interest rates and inflation. Thus, a multivariate regression is adopted. Therefore, an equation is created to help determine the full extent of the role that the independent variables play in the final outcome of the dependent variable.
From the equation above it would be expected that an increase in interest rates would isolate the housing market for consumers since mortgage payments would unattractively increase and thus affect housing affordability and ultimately the demand for housing services would naturally be deflated. On the other hand, an increase in inflation rates would result in an increase in housing services since the costs of goods and services is increasing. However when the inflationary pressures start to take its toll on the economy the house prices affect the affordability. Thus would eventually conclude with the decline in house prices in the real estate market. However an increase in permanent income would result in an increased demand for housing, since households have more disposable income which they can afford on the consumption of luxury goods. Therefore the housing market would predominantly be concerned with the alteration in the income elasticity of demand.
The quarterly data obtained from the UK economy will be analysed by several different tests, but before any analysis can be undertaken, all the variable data sets will need to be converted to the same base levels. Therefore in order to comprehend the results more efficiently the data will be examined, by finding out how ‘good' the fit of the regression analysis is. This will enable one to critically analyse the exact consequence of the economic cycle in terms of the variables under scrutiny. When regression analysis of the data will be carried out by introducing the Ordinary Least Squares method it is assumed that the GaussMarkov theorem is correct. That is that the error terms have a mean value of zero, are homoscedastic and are uncorrelated. Consequently the estimators will result in to Best Linear Unbiased Estimator (BLUE). Before implementing the multivariate regression, several preliminary tests are required to be performed. Regression models can lead to ‘spurious' results whereby the results appear significant. Therefore It is vital to determine the status of the time series data, whether it is stationary or non stationary. Thus, the DickeyFuller test is performed to evaluate the unit root hypothesis. However, regressions that appear to be ‘spurious' (Gujarati 2010) may still have a relationship between the non stationary data and so will be tested for cointegration using the Johansen test.
When conducting the regression, the average house prices will be regressed against interest rates, inflation and income. However when using a time series data in a regression analysis, it is known that the residuals do not meet the criteria that the error terms are uncorrelated. As a consequence the hindrance of autocorrelation may arise. But to overcome this problem the Durbin  Watson statistic test or the Breusch  Godfrey LM test can be executed to check for robustness of serial correlation.
After carrying out the OLS regression, the hypothesis test will be applied to the results in order to prove the statistical relationship between the explanatory and dependent variables. Therefore the significance level will indicate the influence of the parameter. For the analysis of our tests the 5% significance level will be employed. Therefore a pvalue subordinate than 0.01, will incline us to reject the null hypothesis, and indicate that the explanatory variable does have a relationship with the dependent variable. Another predominant indictor to the validity of the results will be the determination coefficient, r2. The determination coefficient of the results can inform the significance of the goodness of fit of the variables. ‘R2 measures the proportion or percentage of the total variation in Y explained by the regression model' (Gujarati 2010). If when analysing the data, multicollinearity is detected. That is that the R2 value is large and with the t test statistic being irrelevant. The large value of the residuals of the explanatory variables would indicate the need to increase sample size or a change in the approach. Nonetheless, the residuals will be tested for normality by using the JarqueBera test and also for heteroscedasticity.
In this section of the paper the empirical results from the data is presented, after using the above suggested model. The results will be critically analysed and will endeavour upon supporting the hypothesis about the UK house prices.
Before analysing the significant values of the model, it is essential that the raw data being used to generate the results is scrutinised. Therefore it is essential to measure the response of the variables discussed in this paper over the time period under investigation. As a result, graphs portraying the fluctuations of both the explanatory and dependent variables over the period of 1980 to 2009 have been illustrated.
Graph 1 in the appendix indicates the trend of average UK house prices over the sample period. From the graph we can see that over the 30 year period there has been minimal variation. The trajectory testifies to the fact that UK house prices have continually thrived since 1980 with minimal fluctuation. The average house price in 1980 was just above £20,000, whereas in 2009 it roughly costs around £150,000. This highlights that house prices have increased by 9 times since the start of the time period. However it is evident that subsequent to 2008, house prices have sharply started to decline. Furthermore, it also emphasizes that there was a property market collapse in the early 1990s, from which the market had to recover over a period of 5 years.
Graph 2 (appendix) illustrates that the national disposable income has steadily increased from the start of the sample period. From the graph it is evident that in 1980 the average national disposable income was just under £100,000. However by 2009 the disposable income had increased to above £200,000. The graphical representation indicates that there is a positive linear relationship over the time period. It also shows that there is negligible fluctuation over the testing period.
Graph 3 (appendix) depicts the graphical representation of the current bank rate being offered by the Bank of England. Generally speaking the bank rate over the 30 years exhibits a weak negative correlation, but without any distinct linear trend. The graph displays constant volatility of the interest rate over the time period. A major peak in the graph occurs over the period of the early 1990s when the bank rate reached 15%, and thus monetary policy was tightened. The bank rate has dropped significantly over the 30 year period with it at an all time low of 1.0% in 2009 over the sample period. In contrast the bank rate on offer at the start of the sample period is significantly high at 17.0%. Overall, indicating to a dramatic reduction of 16.0% over the period, ignoring the fluctuations over this period.
In graph 4 (appendix) the positive correlation indicates that there is a distinct linear relationship between the RPI inflation index and the time period. The visual representation illustrates that there is minimal fluctuation over the sample period. It appears as though towards the latter stages of 2008 inflation seems to be declining ever so slightly, however this seems to be of little significance. Over the sample period, the inflation index has changed from about 60 to about 210, an increase of roughly 250%.
In addition to the graphical analysis, Table 1 (appendix) summarises all the data of the variables under investigation in this paper. It is evident that the measures over the sample period indicate a reasoning of the raw data that is effortlessly comprehendible.
As explained in the methodology, before implementing the regression model, it is imperative to test the assumption that time series data is stationary and therefore avoid achieving ‘spurious regression' (Gujarati 2010). Thus, if the data is stationary, characteristics such as its mean, variance and serial correlation would remain consistent over the time period. Therefore in order to validate our model, the unit root test will be enforced on each set of data. In this case, the augmented DickeyFuller test is applied. The test implies that greater the negative statistical value of DickeyFuller is achieved, the greater the inclination to reject the null hypothesis.
Thus the following equation is estimated:
The null hypothesis for this test is that the data is nonstationary. That is γ is zero. Whilst the alternative hypothesis is that there is no unit root and the data is stationary. That is γ is smaller than zero. Therefore:
Thus, whilst using this test if the tvalue for each variable coefficient is larger than the augmented DickeyFuller value we reject the null hypothesis. On the other hand, if the tvalue is smaller, we accept the null hypothesis, and argue that the data is nonstationary.
Having applied the unit root test to the variables under investigation, the augmented DickeyFuller test statistic for each variable is greater than the critical 5% confidence interval. This occurred when all the variables are tested for unit root at base level. Therefore, as shown in the appendix, the DickeyFuller test value for average UK house prices is 1.185358, which is greater than the 5% critical value of 2.886732. Hence we have to conclude that the data series is nonstationary and accept the null hypothesis that there is a unit root. Likewise it is similar for the other explanatory variables. Therefore we have to perform the test for unit root at the first difference of each variable. The results of which are presented below.
Average UK House Prices:
Null Hypothesis: D(PRICESS) has a unit root 

Exogenous: None 

Lag Length: 0 (Fixed) 

tStatistic 
Prob. 

Augmented DickeyFuller test statistic 
2.932764 
0.0037 

Test critical values: 
1% level 
2.585226 

5% level 
1.943637 

10% level 
1.614882 

MacKinnon (1996) onesided pvalues. 

Thus from the table above we are interested in the generated tvalue at the critical 5% confidence interval. Therefore, we can infer the reasoning behind the values computed in the table. It highlights that the calculated DickeyFuller value of 2.932764 is statistically significant since it is lower than the tested 5% critical value of 1.943637. In fact it is lower at all the confidence intervals. This analysis leads to the conclusion that this average house prices data set appears to be stationary and thus leads to the rejection of our null hypothesis and so there is no unit root. So, the data is stationary at the first difference and incorporated at order 1.
Disposable Income:
Null Hypothesis: D(INCOMESS) has a unit root 

Exogenous: None 

Lag Length: 0 (Fixed) 

tStatistic 
Prob. 

Augmented DickeyFuller test statistic 
11.20828 
0.0000 

Test critical values: 
1% level 
2.585226 

5% level 
1.943637 

10% level 
1.614882 

MacKinnon (1996) onesided pvalues. 

The DickeyFuller test statistic of 11.20828 is also statistically significant, since the 5% critical tvalue of 1.943637 is greater than the DickeyFuller value. This interpretation concludes that the disposable income is stationary at the first difference level and is incorporated at order 1. Thus, once again the null hypothesis can be disregarded.
Interest Rate:
Null Hypothesis: D(INTEREST) has a unit root 

Exogenous: None 

Lag Length: 0 (Fixed) 

tStatistic 
Prob. 

Augmented DickeyFuller test statistic 
9.886140 
0.0000 

Test critical values: 
1% level 
2.585226 

5% level 
1.943637 

10% level 
1.614882 

The data for interest rate appears to be stationary at the first difference and order 1. The DickeyFuller value of 9.886140 is less than 1.943637 at the 5% critical value. It is also evident that the critical DickeyFuller value is lower than the other two tstatistic confidence intervals.
Inflation Rate:
Null Hypothesis: D(INFLATION) has a unit root 

Exogenous: None 

Lag Length: 0 (Fixed) 

tStatistic 
Prob. 

Augmented DickeyFuller test statistic 
5.700171 
0.0000 

Test critical values: 
1% level 
2.585226 

5% level 
1.943637 

10% level 
1.614882 

MacKinnon (1996) onesided pvalues. 

The calculated DickeyFuller value of 5.700171 is statistically significant since it is lower than the tested 5% critical value of 1.943637. In fact it is lower at all the confidence intervals. Therefore the data for inflation rates appears to be stationary. Thus the null hypothesis is rejected and so there is no unit root. Therefore, the data is stationary at the first difference and incorporated at order 1.
As a result of the unit root being tested in the first difference, all the variables in the model are stationary at order 1.
Regardless of the fact that the time series variables at the base level emphasised that the series were nonstationary. It is feasible that there is a statistically significant linear relationship between the variables which would indicate that there is cointegration. Hence there is potential that a long run equilibrium correlation exists between the nonstationary variables. Therefore the Johansen test will be employed for this hypothesis. The results of which are tabulated below.
Date: 03/16/10 Time: 14:09 

Sample (adjusted): 1981Q2 2009Q1 

Included observations: 112 after adjustments 

Trend assumption: No deterministic trend 

Series: PRICESS INCOMESS INFLATION INTEREST 

Lags interval (in first differences): 1 to 4 

Unrestricted Cointegration Rank Test (Trace) 

Hypothesized 
Trace 
0.05 

No. of CE(s) 
Eigenvalue 
Statistic 
Critical Value 
Prob. 
None 
0.229410 
58.35518 
40.17493 
0.0003 
At most 1 
0.131765 
29.16818 
24.27596 
0.0112 
At most 2 
0.075004 
13.34336 
12.32090 
0.0336 
At most 3 
0.040335 
4.611199 
4.129906 
0.0377 
Trace test indicates 4 cointegrating eqn(s) at the 0.05 level 

denotes rejection of the hypothesis at the 0.05 level 

MacKinnonHaugMichelis (1999) pvalues 
The tabulated results of the Johansen cointegration testing technique indicates that at the 5% critical value there are 4 cointegrating equations when the trace test is applied. The trace statistics produces significant values that are greater than the 5% confidence intervals shown in column 3 of the table. Thus, we can determine that although the time series for all the variables is nonstationary, linear combinations seem to exist between several variables. Therefore it can be assumed that there may be longrun relationships between the individual variables under investigation. As a result, this reasoning reduces the possibility of achieving spurious results when conducting regression analysis.
Prior to demonstrating the response of average UK house prices in a multivariate regression, by incorporating the time series variables. It is essential to highlight the association of the individual explanatory variables on the dependent variable using a bivariate regression model. Thus, the method of ordinary least squares is adopted to estimate a model of house prices, since the least square principle minimises the residual sum of squares.
Dependent Variable: LOG(PRICESS) 

Method: Least Squares 

Date: 03/21/10 Time: 20:00 

Sample (adjusted): 1980Q1 2009Q1 

Included observations: 117 after adjustments 

Variable 
Coefficient 
Std. Error 
tStatistic 
Prob. 
C 
7.200685 
0.301326 
23.89669 
0.0000 
LOG(INCOMESS) 
2.278458 
0.060527 
37.64336 
0.0000 
Rsquared 
0.924936 
Mean dependent var 
4.127190 

Adjusted Rsquared 
0.924283 
S.D. dependent var 
0.609698 

S.E. of regression 
0.167769 
Akaike info criterion 
0.715515 

Sum squared resid 
3.236829 
Schwarz criterion 
0.668298 

Log likelihood 
43.85760 
HannanQuinn criter. 
0.696345 

Fstatistic 
1417.023 
DurbinWatson stat 
0.048064 

Prob(Fstatistic) 
0.000000 

The calculated output indicates that the intercept or parameter β1 equals to 7.200685. On the other hand the slope coefficient for the variable income equals 2.278458. Hence the income elasticity indicates that a 1% increase in disposable income results in a 2.28% increase in average UK house prices, assuming all other factors remain constant. The pvalues are all lower than the critical 5% value indicating that the null hypothesis can be rejected. The R2 value of 0.92 is significant as it shows the goodness of fit for the regression line. 92% of the variation in house prices is explained by the explanatory variable. This measured response explains the behaviour of house prices in relation to disposable income, which incidentally supports the theory. Thus an increase in household income increases the demand for housing services.
Dependent Variable: LOG(PRICESS) 

Method: Least Squares 

Date: 03/21/10 Time: 20:04 

Sample (adjusted): 1980Q1 2009Q1 

Included observations: 117 after adjustments 

Variable 
Coefficient 
Std. Error 
tStatistic 
Prob. 
C 
6.160335 
0.159916 
38.52240 
0.0000 
LOG(INTEREST) 
1.015858 
0.077857 
13.04774 
0.0000 
Rsquared 
0.596836 
Mean dependent var 
4.127190 

Adjusted Rsquared 
0.593330 
S.D. dependent var 
0.609698 

S.E. of regression 
0.388808 
Akaike info criterion 
0.965486 

Sum squared resid 
17.38478 
Schwarz criterion 
1.012703 

Log likelihood 
54.48093 
HannanQuinn criter. 
0.984655 

Fstatistic 
170.2436 
DurbinWatson stat 
0.150791 

Prob(Fstatistic) 
0.000000 

The tabulated results show that the intercept or parameter β1 equals to 6.160335. The value for slope coefficient for the variable equals 1.015858. Hence the rate of change indicates that a 1% increase in interest rates results in a decrease of 1.02% in average UK house prices, assuming all other factors remain constant. This provides evidence to the theory that an increase in interest rates deters potential customers from borrowing due to the higher mortgage payments, resulting in lower house prices.
Dependent Variable: LOG(PRICESS) 

Method: Least Squares 

Date: 03/21/10 Time: 20:07 

Sample (adjusted): 1980Q1 2009Q1 

Included observations: 117 after adjustments 

Variable 
Coefficient 
Std. Error 
tStatistic 
Prob. 
C 
4.346442 
0.314094 
13.83801 
0.0000 
LOG(INFLATION) 
1.728695 
0.063936 
27.03774 
0.0000 
Rsquared 
0.864073 
Mean dependent var 
4.127190 

Adjusted Rsquared 
0.862891 
S.D. dependent var 
0.609698 

S.E. of regression 
0.225761 
Akaike info criterion 
0.121736 

Sum squared resid 
5.861307 
Schwarz criterion 
0.074520 

Log likelihood 
9.121568 
HannanQuinn criter. 
0.102567 

Fstatistic 
731.0394 
DurbinWatson stat 
0.017966 

Prob(Fstatistic) 
0.000000 

The output shows that the slope coefficient, β2, is estimated to equal 1.728695, whilst the estimation for the constant term is 4.346442. This leads to the inference that a 1% increase in inflation results in an increase of 1.73% in average house prices, holding all other variables constant. The R2 value shows that 86% of the independent variable explains the variation in house prices. Hence an increase in inflation produces increases in prices of goods and services, including housing.
As explained in the theory, the dependent variable for this model is responsive to several explanatory variables. The model suggested in the methodology incorporates this theory and develops the simple linear regression theory into a multiple regression model. Once again the OLS method will be adopted to construct reasoning from the model.
Dependent Variable: LOG(PRICESS) 

Method: Least Squares 

Date: 03/21/10 Time: 20:08 

Sample (adjusted): 1980Q1 2009Q1 

Included observations: 117 after adjustments 

Variable 
Coefficient 
Std. Error 
tStatistic 
Prob. 
C 
10.03835 
0.698542 
14.37044 
0.0000 
LOG(INCOMESS) 
3.297483 
0.291609 
11.30789 
0.0000 
LOG(INTEREST) 
0.221210 
0.059533 
3.715731 
0.0003 
LOG(INFLATION) 
0.544985 
0.217083 
2.510493 
0.0135 
Rsquared 
0.936236 
Mean dependent var 
4.127190 

Adjusted Rsquared 
0.934544 
S.D. dependent var 
0.609698 

S.E. of regression 
0.155988 
Akaike info criterion 
0.844486 

Sum squared resid 
2.749542 
Schwarz criterion 
0.750053 

Log likelihood 
53.40245 
HannanQuinn criter. 
0.806148 

Fstatistic 
553.0565 
DurbinWatson stat 
0.114630 

Prob(Fstatistic) 
0.000000 

The estimated output indicates that the constant term or parameter β1 equals to 10.03835. It also indicates that out of the three explanatory variables under investigation, disposable incomes give the strongest indication to influencing the dependent variable with a coefficient value of 3.297483. At the same time, inflation rate is the weakest variable to affect house prices at 0.544985. Analysis of the income elasticity indicates that a 1% increase in disposable income results in a 3.30% increase in average UK house prices. The table also shows that the pvalues are all lower than the critical 5% value indicating that the null hypothesis can be rejected. The R2 value is significant as it shows the goodness of fit for the regression. Thus 93% of the variation in the dependent variable is illustrated by the explanatory variables. However the table gives evidence to the presence of serial correlation between the residuals, as shown by the DurbinWatson statistic. The value of 0.114630 is suggestive of positive correlation occurring. The BreuschGodfrey test was conducted in support of the finding (appendix). However, we will assume that there is no serial correlation for the regression analysis at all
Having estimated the regression, it is essential to test the residuals of the data set for normal distribution as this will highlight problems with the regression model.
The histogram produces a general ‘bellshape, with an insignificant JarqueBera statistical value, and a large pvalue. This inference leads us to the conclusion that the regression model appears to potentially be correct. It is possible that this may be flawed due to the serial correlation discovered in the ordinary least squares method or due to another factor. Another assumption made when carrying out the regression model is that the residuals variance is homoscedastic, as shown when the ARCH test of heteroscedasticity is performed (Appendix).
Upon discovery of serial correlation when the multivariate regression was estimated, the assumption was taken that there was no serial correlation, as should be the case under the classic linear regression model. This assumption was adopted in order for the ordinary least squares method to produce best linear unbiased estimators. However, the results were in fact flawed due to the presence of serial correlation. That is the residuals of one variable may influence the residuals of another variable. But there may be several reasons for the occurrence of serial correlation in time series data. A characteristic of time series data is inertia, whereby the variables go through economical cycles and so regression estimates exhibit correlation.
Another possible reason may be the technique in which the raw data is manipulated to represent quarterly data of the variable. On the other hand, it is possible that the regression model was not specified accurately.
Another assumption made under the classic linear regression model, when using the OLS method is that the residuals have minimum variance. That is they are homoscedastic. However as the ARCH test showed the variances indicated heteroscedasticity. This resulted in the estimators being inefficient. However the estimators remain unbiased (BLUE).
In summary, the regression model supports our hypothesis taking into account the assumptions taken as discussed above. The results of the investigation support the theory framework carried out prior to the analysis of the raw data for each time series variable. Thus an increase in household income increases the demand for housing services. However, an increase in interest rates deters potential customers from borrowing from financial institutions due to the higher mortgage payments, forcibly resulting in decrease in house prices. But the deviation in inflation can result in both house prices increasing and falling. An increase in inflation produces increases in prices of goods and services, including housing. However this increase may also result in house prices growing further, as well as other consumable services and so the growth in income and services may not be sufficient enough thus inevitably resulting in house price falls.
In order to make this summary, some of the limitations highlighted were suppressed. But apart from this, it was discovered that the raw data series were all non stationary at the base level and displayed unit roots. Thus alterations were conducted at the first difference to validate the data. The discovery of cointegration equation also indicated that the variables were all interdependent. This issue was further highlighted by the presence of serial correlation as discussed above. Nevertheless in order to agree to the GaussMarkov assumptions and the CLRM, assumptions were made to validate the regression analysis using the least squares method.
In this paper, macroeconomic raw data is used to estimate the response of UK house prices with particular significance given to the affects of income, interest rates and inflation upon house prices. Thus an equation for UK house prices was developed investigating the elasticity in demand for housing.
From the results, it can be suggested that the role of the explanatory variables to explain fluctuation in house price movement is significant. The regression model estimated that the most significant variable under enquiry was that of disposable income. The estimated elasticity of demand for average house prices when using disposable income is 3.30%, controlling all other variables. This suggests that monetary issues are by far the most significant determinant of house price movement. The large value for income from the derived equation suggests that in order to enter the real estate market a potential customer needs to have disposable income to purchase housing and its associated services. It also suggests that the other variables under investigation are interdependent between all the explanatory variables. This is supported by our results indicating cointegration between average house prices and the explanatory variables.
Low interest rates encourage potential customers from borrowing from financial institutions as they are can meet their mortgage payments. The low rate therefore initiates greater number of customers to make a housing investment. Hence, it has an elasticity of demand value of 0.22%. However if potential borrowers have a low amount of disposable income, the low interest rates is ineffective. Therefore house price movements should steadily plunge. Therefore the low interest rate would encourage inflationary pressures to heighten. Increased inflationary pressure increases prices of goods and services, including housing. However this increase may also result in house prices growing further, as well as other consumable services and so monetary growth is all so required.
The findings of our model are consistent with the theory. However as explained above the interdependency of the input does not isolate each individual variable and thus it is difficult to highlight the effect of the independent variables on the responsive variable. Also in order to validate the results of the multivariate regression with greater statistical significance, the data range could have been extended. However it was difficult to locate the data for average house prices pre1980. Finally, since the data exhibits cointegration, the model could have been extended to include more influential variables. In view of the fact that our results show that the data is nonstationary at base level and shows correlation.
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