This project intend to analyze the real estate London market behavior and detect the presence of bubbles. The real estate market usually presents a caractheristic cylce with two important phases: a rapid increase of house prices, called as “boom”“, until a certain level, followed by a fast decline called as”bust“. If the house prices raises more than expected in the boom phase and falls faster than the fundamentals suggest in the bust phase, we have a bubble. A lot of variables are associate to the occurrence of bubbles, such as rent prices, mortgage and interest rates, credit volumes, industrial production, asset prices and similar variables related with real estate supply and demand. In this report, we intend to detect bubbles in the London real estate market and create a model capable of determinate the strength of the relationship between house prices and some selected variables.
In this report, 5 variables were selected to compose our dataset: the average house prices, the gold price, the unemployment rate, the FTSE 100 and the interest base rate. The data were taken mostly from Quandl Fincancial and Economic Data and has 8 columns and 69 rows. The dataset comprises data between the \(1^{st}\) of October 2010 and the \(30^{th}\) of June 2016.
To fit a model, firstly we should determine whether our data is stationary. In case the answer is no, we need to determine the order of differencing to achieve stationary data. The ADF test result indicates stationarity if the p-value \(<\) 0.05. The table below shows the p-value for every variable and the graph represents the behavior of the series.
## Avgprice Gold Unemployment Interest Rate FTSE 100
## P-value 0.01 0.7063733 0.2197732 0.4933662 0.6251907As we can see, the series are not stationary. So we differentiate until it becomes stationary. In this case, 2 differentiations were necessary. The p-values and a graph with the diferentiated series are showm below.
## Avgprice Gold Unemployment Interest Rate FTSE 100
## P-value 0.01 0.01 0.01 0.01 0.01It tooks 2 differentiations levels to make data stationary. Once we have a stationary dataset we need to determine how many lags will be included in the model.
A common model used in the real estate market is the VAR or VECM model. To select how many lags should be included in those models, we first estimate an unrestricted VAR model and select the model with smaller AIC, HQ, SC, or FPE.
## AIC(n) HQ(n) SC(n) FPE(n)
## 9 9 9 9The criterions shows that the VAR model with 9 lags is the most appropriate one.
The last step is the cointegration test. The detection of cointegration between nonstationary variables is important since if there is a cointegration, a VAR model with first differences is misspecified. If there is a cointegration, a VECM model should be applied. The Johansen test will be used to check ih thre is cointegration between the variables. The cointegration tell us if the variables presents a long-term relationship.
## r trace trace_pval trace_pval_T eigen eigen_pval
## 1 0 294.9612286 < 0.001 <0.001 146.0248255 < 0.001
## 2 1 148.9364031 < 0.001 <0.001 72.8957831 < 0.001
## 3 2 76.0406201 < 0.001 <0.001 60.8215731 < 0.001
## 4 3 15.2190470 0.05352 0.1144 14.5205736 0.04353
## 5 4 0.6984733 0.40330 0.4647 0.6984733 0.40330The Johansen Test show us that there is at most 2 cointegration. It means that, at least three variables are related in a long-term relationship.
Another common analysis that can be applied to the VAR/VECM models is the causality analysis. The Granger test is used in the respective model to check if a variable X “Granger-causes” Y. It happens if the past values of X helps to predic the atual value of Y.
Applying the Granger causality test and changing the variables is possible to identify that the combination of the Gold prices, Unemployment rate and Interest Base rate “Granger-cause” Average House Prices. The p-value for this case is 0.0283682. It means that the average house price in London can be explained by a combination of these variables or that the variation of these variables causes the variaton of the house prices.