Econometric Analysis of the Relationship Between

Macroeconomic Variables and UK House Prices

_________________________________________________________________________

Alex Abrahams

Matt Cooper Tom Ingram Ted Moore

Sam Portmann

Abstract In this project, we estimate and simulate a multivariate model of quarterly UK housing prices over the period 1995-2010. The initial model was formed by M. Baddeley and D. Barrowclough (2009), we intend to recreate their model and run the regression with our data, further we will add variables in an attempt to assess the elasticities in housing prices. The overall purpose of this project is to see whether UK housing prices are driven by long-term fundamental macroeconomic changes rather then speculative reasons.

Table of Contents

 1. Introduction ........................................................................................................ 1 2. Theory ................................................................................................................ 1 3. Literary Review .................................................................................................. 2 4. Methodology ...................................................................................................... 2 5. The Econometric Model of House Prices ........................................................... 3

• Reproducing the original model • Modifications to the model • Diagnostic testing • Granger causality

6. Analysis .............................................................................................................. 6 7. Limitations .......................................................................................................... 7 Bibliography ........................................................................................................... 8 Appendix ................................................................................................................ 9

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1. Introduction Housing is usually the single biggest lumpy good purchase for a consumer and being such an expensive necessity that’s widely consumed, changes in the economy can have major impacts on consumer equity. Further, in recent years housing has increasingly been seen as an investment asset both to hedge against inflation and to generate income on the rental market. Speculators have also seen a rise in returns following the housing bubbles particularly in the South-East encouraging additional investment and demand-led price rises. Macroeconomic variables have significant changes in consumer purchasing power; whether it’s availability and affordability of credit; in relation to income elasticities or relative prices of housing to consumer wealth. Using time series econometrics we develop a model to explain and forecast the long run implications of changes in macroeconomic variables on property prices and its fundamental causes. 2. Theory The principle endogenous variables used and expected relationships in the model are: • FTSE all-share index, used as a proxy to reflect the current economic conditions. • GDP (ONS) - quarter on quarter growth. A greater GDP leads to a higher GDP per capita

(assuming population constant). The higher GDP per capita, the greater demand for houses and hence house prices will rise.

• Lending (Bank of England) as a total secured gross lending to individuals and housing associations. Again, the theory derives from supply and demand - a higher availability of credit pushes up house prices.

• Average interest rates (Bank of England). Most houses are purchased through credit and therefore a higher rate of interest will lower demand for mortgages. In addition, changes in buying preferences may change when consumers may prefer to save when banks are paying higher rates.

• Real effective exchange rate (Bank of England). Based on economic theory, the relationship between house prices and the exchange rate should be negative. If the exchange rate rises, a stronger pound would put upward pressure on the price of houses and decrease housing demand from abroad. We have used a weighted average of the UK exchange rate’s movements against a basket of currencies for the purpose of this project.

• Inflation – CPI (ONS). It is expected that there would be in positive relationship between house prices and inflation. This can be explained by the overall increase in prices when there is inflation and housing being a normal good should also see price rises. Furthermore, Irving Fisher stated that r = i - E𝜋. Real interest rates should decrease as expected inflation increases, assuming nominal rates don’t rise at the same rate as inflation. Therefore, lower interest rates would increase house prices. With sustained inflation, investors will be drawn into the property market with the view of continued appreciation of prices and hedge against inflation.

• Average UK house prices (Nationwide) - dependent variable.

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3. Literary Review Looking at our housing price data, in quarter 4 2010 the house price index was £162,971 and in quarter 11995 the house price index was £51,084, which is a 319% increase in house prices over the period. Literatures such as Anderrson (2014) talk about stock prices having a significant positive correlation on house prices. GDP and interest rates were used as control variables and these did not affect the overall causality. A paper by Meldani (2011) suggests there was no Granger causality between real house prices and CPI. However, Goodhart and Hofmann(April 2008) then go on to say that GDP, CPI and interest rates have a significant effect on house prices. Valdez (2011) agreed with Goodhart and Hofmann (April 2008) that GDP has a significant effect on house prices but also mentioned that there may have been other causal factors in that conclusion. A paper by Mahalik and Mallick suggests that exchange rates having a Granger causal effect on house prices, however this may not hold in the long run. In summary, the papers mentioned and many others seem to each have contradicting results. This could be due to slightly different methodology used, timeframes and countries. 4. Methodology We begin by estimating the model by M. Baddeley and D. Barrowclough (2009). This model aimed to assess the various determinants of fluctuations in UK housing demand, with a particular focus on credit constraints. We then modify the model by adding variables relevant to the macroeconomy in order to gain a wider perspective on changes in housing prices and where policies should be implemented. Granger, Newbolds (1974) and Phillips (1986) have shown that results may be spurious if the estimated variables are non-stationary and don’t display cointegration, this would invalidate testing and inference from the results. Using the Augmented Dickey-Fuller Unit Root test we tested the stationarity of the variables. Variables are considered cointegrated if they share a stochastic drift with one another, indicating that the relationship between the variables is not spurious. Model mis-specification can be critical in terms of the unfavourable outcomes on the sampling properties of estimators and subsequent tests. In addition, further inference and estimation based on the model will be erroneous. We will use general-to-specific methodology with the main aspects of this approach to assess dynamic specification, variable selection, functional form and in order to achieve the BLUE model. The dynamic nature of our model is cause for including lagged variables in order to capture the time between the change in economic conditions and movement of house prices. AIC values will be used to determine the optimum lag for each variable. Lastly, the Granger (1969) causality test will be conducted in order to determine the models

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application to forecasting future values of housing prices based on the time series data and comparing the power of the model with intuition. 5. The Econometric Model of House Prices Firstly, we started by estimating the model by M. Baddeley and D. Barrowclough (2009) in Running Regressions (Appendix 1). This model gave estimations in assessing housing demand backed by credit. Firstly, a single hypothesis test must be run - in terms of c, loglend and logrates resulting in a P-value = 0. For these values the null hypothesis, the observed difference is due to sampling error is rejected. The adjusted R squared is a goodness of fit measure which additional explanatory variables by using a degree of freedom adjustment. The adjusted R squared figure is 0.863466, meaning 86.3% of the variation in the model is explained by the explanatory variables, this shows there is certainly some relationship between the independent and dependent variables. We found this model to be limited in many respects. Indications were present that many of the Guass-Markov assumptions had been violated and problems with the residuals. Credit availability is a main factor in the demand for housing; although we wish to expand this model further and explore more general affecting factors linked to policy implications and macroeconomic changes. We therefore added various macroeconomic variables to the model. We removed the highly insignificant variables as well as variables deemed irrelevant and if removed wouldn’t impact the overall significance of the model. Variables that were originally in the model but subsequently removed were: employment rate, output per worker, PSNB, disposable income, PE ratio, and seasonal dummy variables. The first stage was to test the data for stationarity using the ADF test.

H0: variable has a unit root.

The variables were tested at the level form and after a failing to reject the null hypothesis, tested for a unit root in the 1st difference - all of which rejected the null. We conclude that the variables are non-stationary in their level form and stationary in their 1st difference - I(1). However using the 1st difference loses the long-term trends in the data, therefore we proceeded to test for cointegration. ARDL approach as sample is reasonably small, using the Wald Test:

H0: C(2)=C(3)=C(4)=C(5)=C(6)=C(7)=0

F-statistic: 20.37262, (4, 53): P=0 ‘@TREND’ has been added in order to estimate the trend. We compare the F-statstic to the critical value of the table Pesaran et al (1999) for intercept and trend at I(1) - 3.614. The F-statistic is higher then the upper bound, therefore the data has long run associations and

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cointegration. We can continue the estimation using level form variables as the nature of the project is only interested in long run relationships. The model has been put through several diagnostic tests to address the degree to which it identifies with empirical evidence and with a focus on ‘variable addition’ methods, to evaluate the significance of each chosen variable. Ramsey RESET test: General test for specification errors in the linear regression. Under any of these errors, resulting least squares estimators will be biased, inconsistent and inference invalid.

H0: the model is correctly specified

Conducting the RESET test results in a rejection of the null hypothesis in the ‘linear-linear’ model. Observing the scatter plots between PRICES and each independent variable reveals that the model is most likely is non-linear and should be converted to ‘log-log’, this is also useful in calculating elasticities. Taking logs and re-running the RESET test yields a slightly higher P-value, however again the null is rejected indicating the mis-specification could be due to significantly non-linear relationship. Lagging the IVs using the lowest value of the AIC, the model is defined as:

logPRICE = C + β1logLEND + β2logRATES + β3GDP(-4) + β4logER + β5logCPI + β6logFTSE(-

4) + β7logPRICE(-1) Where ‘C’ is the intercept and βi is the respective coefficient.

F(2,50)=0.8958

P-value1 = 0.4147

With the P-value higher then 0.05, we fail to reject the null hypothesis and can conclude that with the lags and logged variables, the functional form is correct. Heteroskedasticity - Breusch-Pagan-Godfrey Test:

H0: errors are homoskedastic

Prob F(7,52) = 0.0882 > 0.05 fail to reject null.                                                                                                                1  Throughout the project we will report a P-value as they are easier to use and are provided in Eviews.  

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Q-statistics, LM Test:

H0: there is no serial correlation

In the correlogram, the Ljung-Box Q-statistics show for the first 10 lags P-values all to be 0 and PAC/AC not close to zero. The spikes are also indicative of serial correlation in the model.

Likewise, the P-value calculated for Breusch-Godfrey LM Test rejects null. Despite this, OLS estimates are still unbiased and consistent. The problem being that the model is not BLUE and therefore inefficient, the standard errors are also invalid. Serial correlation in time series data is not uncommon as ordered data tends to have correlated error terms. We need to remove the serial correlation in order to estimate the dynamic model. To do this we have included a lagged dependent variable in the RHS of the equation. This benefits the model for two reasons; the first is that dynamic effects are now captured and second, 1st order serial correlation has been removed. The LM test now has a P-value of 0.2524 and we can fail to reject the null, concluding there is no serial correlation in the model. Note: Durbin-Watson statistic2 is now 1.66. Estimation output - see Appendix 2.                                                                                                                

2  d = Σ(εt −εt−1)2

Σε 2t  

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Granger Causality:

Variable P-value Fail to reject/reject H0 Variable Granger Causes Price

Lending 0.0301 Reject Yes Rates 0.0103 Reject Yes GDP 0.4532 Fail No FTSE 0.3608 Fail No

Exchange rates 0.555 Fail No Inflation 0.0015 Reject Yes

6. Analysis We found that a one percent increase in interest rates estimated a -1.2661% decrease in house prices. This was as expected - if rates rise, mortgage payments increase and consumers may face negative equity and defaulting. This seems to be the dominant theory, another being that house prices could continue to rise on high consumer confidence and if household incomes were high. This sensitivity is perhaps due to the extremely low-income growth during the recession. This ties in with the results we estimated for lending - a one percent rise in lending leads to a 6.2431% rise in house prices. This was as expected according to our economic theory, due to the volatility in house prices being driven by supply and demand, more lending implies an increase in demand and therefore and upward pressure on house prices. The coefficient of GDP estimated that a one percent increase in GDP leads to 0.9% decrease in house prices, ceteris paribus, this contradicts our intuitive theory. However GDP is made up of many components and one of these components may affect house prices more then another. Further, the Granger causality test results show that GDP does not Granger cause house price, which again, is not what was expected. In theory, between CPI and house prices there should be a positive relationship. We found a one unit increase in the CPI causing a 0.44% increase in the price of houses - cetreris paribus - in keeping to our theory set out at the start of the project. The Eviews output gave the exchange rate a coefficient of 0.233730 - a one unit increase in the exchange rate, would lead to a 0.23% increase in the price of houses, keeping the other variables constant. This again contradicts our theory, as we would expect a decrease in the price of housing instead of an increase. In summary, our econometric analysis has shown that interest rates, lending and inflation all affect house prices according to our theory. Surprisingly, the estimation revealed changes in GDP and exchange rates have no affect on UK housing prices. This implies policy makers should focus on three particular factors in relation to the housing market. Interestingly, the variables that model suggests affects house prices the most, lending and interest rates were both a main factor in the recent financial crisis. Initially affordable subprime mortgages were repackaged as MBS and CDOs as investment products and subsequently insured. As interest rates rose, these became

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increasingly unaffordable causing widespread defaults in the property market with effects rippling though the world economies. 7. Limitations The model that has been used does have its limitations. Although a wide range of variables have been used in the model, there are still numerous factors that can have an influence on house prices that haven’t been taken into consideration. There are aspects associated with the demographics of the UK which can alter housing demand, such as marital status/age at which people get married, age structure and net migration. These are unrelated to either speculation or macroeconomic changes and are usually unquantifiable. At times the coefficients produced by the model can suggest a relationship between a particular variable and house prices which is intuitively incorrect as we saw with exchange rates and GDP. Particularly with exchange rates, this could be due to the data used. The chosen data set was a basket of weighted currencies - perhaps a more rigorous choice of relevant currencies should have been chosen. Word count: 2,495 Excluding contents page, footnotes, bibliography and appendices.

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Bibliography Charles Goodhart and Boris Hofmann. (April 2008). House prices, money, credit and the macroeconomy. Working Paper Series. 888, p.31-32 Mantu Kumar Mahalik, Hrushikesh Mallick. What Causes Asset Price Bubble in an Emerging Economy? Some Empirical Evidence in the Housing Sector of India. p.21 Jeffrey M. Wooldridge, 2012. Introductory Econometrics: A Modern Approach (Upper Level Economics Titles). 5 Edition. South-Western College Pub. Part 2, Multiple Linear Regression. Mohamed, S, 2009.  Causality Between Property Price and Macroeconomic Variables: An Application of Vector Error Correction and Variance Decomposition Methods to Malaysia. [Online]. Available at: http://www.academia.edu/2309972/  causality_between_property_price_and_macroeconomic_variables_an_application_of_vector_error_correction_and_variance_decomposition_methods_to_malaysia [Accessed 14 April 2015]. Michelle C. Baddeley and Diana V. Barrowclough, 2009. Running Regressions: A Practical Guide to Quantitative Research in Economics, Finance and Development Studies. 1 Edition. Cambridge University Press. Ch. 5,9,10 Erik Andersson. (2014). The Relationship Between House Prices and the Stock Market. An investigation of the American markets. Ali A. Naji Meidani. (2011). House prices, Economic Output, and Inflation Interactions in Iran. p.3, 9 Ray M. Valadez . (2011). The housing bubble and the GDP: a correlation perspective. p.7 Liew, Venus Khim−Sen, (2004) "Which Lag Length Selection Criteria Should We Employ?." Economics Bulletin, Vol. 3, No. 33 pp. 1−9 Utkulu, U (2012). “How to estimate long-run relationships in economics,” an overview of recent development. Retrieved 15/4/2015: kisi.deu.edu.tr/utku.utkulu/dosyalar/How_to_estimate.doc Steinar Strøm, 1999. Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposium (Econometric Society Monographs). Edition. Cambridge University Press. Ch. 11 Data Sources: Office for National Statistics 2014, Key Economic Time Series Data. Available from: <http://www.ons.gov.uk/ons/site-information/using-the-website/time-series/index.html#3> Nationwide 2015, House Prices Index. Available from: <http://www.nationwide.co.uk/about/house-price-index/download-data#xtab:uk-series> Bank of England 2015, Statistics. Available from: <http://www.bankofengland.co.uk/statistics/Pages/default.aspx>

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Appendix Eviews estimation outputs:

2.

1.

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Detailed Calculations: Elasticity workings:

Dependent Variable

Independent Variable Interpretation of β!

y 𝓍 ∆y = β!∆𝓍 y log𝓍 ∆y = (β!/100)%∆𝓍

log  y 𝓍 %∆y = (100β!)∆𝓍 log  y log𝓍 %∆y = β!%∆𝓍

t-Test working (Two-tail alternative): Null Hypothesis: Η!  :  β! = 0 Η!  :  β! ≠ 0 Degrees of Freedom = (64−𝓃) Using 5% critical region value = 2.000

t!! =  !!!!!!"(!!)

t!!"#!$%& =0.062431− 00.019288

= 3.2368 2.368 > 2.000

t!!"#$% =−0.012661− 00.002577

= −4.9139 4.9139 > 2.000

t!!"#(!!) =−0.009297− 00.003774

= −2.4635 2.4635 > 2.000

t!!"#$%&'(!!) =−0.042951− 00.014976

           = −2.8680 2.368 > 2.000

t!!"#$%& =0.441409− 00.176473

= 2.5013 2.5013 > 2.000

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t!!"#$% =0.233730− 00.049800

= 4.6934 4.6934 > 2.000

t!!"#$%&'((!!) =0.829478− 00.042314

=19.60294 19.60294 > 2.000 F-test working: Ramsey Reset test: Null Hypothesis 𝛨!  :  𝑓𝑖𝑡𝑡𝑒𝑑! = 0  𝑓𝑖𝑡𝑡𝑒𝑑! = 0 𝛨!  :  𝑓𝑖𝑡𝑡𝑒𝑑! ≠ 0 𝑓𝑖𝑡𝑡𝑒𝑑! ≠ 0   Value

𝑆𝑆𝑅!" Unrestricted sum of squared residuals 0.01066579004912866 𝑆𝑆𝑅! Restricted sum of squared residuals 0.01104798734822319 𝑑𝑓!" Unrestricted degrees of freedom 50 𝑑𝑓! Restricted degrees of freedom 52

𝑞 = 𝑑𝑓! − 𝑑𝑓!"   Number of coefficient restrictions 2

𝐹 =  𝑆𝑆𝑅! − 𝑆𝑆𝑅!" 𝑞𝑆𝑆𝑅!" 𝑑𝑓!"

       =  (0.01104798734822319− 0.01066579004912866) 2

0.01066579004912866 50

     = 0.8958485432          = 0.895849   Literature Review Working: £162,971  £51,084 ×100 = 319.03%