This study detects explosive behavior and bubbles in US and EU property markets, specifically the EU countries examined are the UK, Finland, Italy, France, Denmark, Germany and Spain. These tests are applied to the data sets from OECD of real house prices, nominal house prices to rent ratio and nominal house price to income ratio for the period from 1980 to 2014. Keywords: Bubble, house prices, SAW, GSAW, right-tailed unit root tests, date-stamp bubble periods, price -to-rent ratio, price-to-income ratio.
Introduction
- Why detecting a house bubble is important?
- Bubble definition
- Colorful adjectives for bubbles
- Conditions of emergence and classification
However, if the increase in housing prices is accompanied by a decrease in the risk premium, then there is not a bubble but a logical response from the market. Another link is between asset prices and the overall stability of the financial and banking system. The direct bubble detection test is designed to confirm or disprove the existence of a bubble, while the indirect tests contrast the current price with the underlying price of the house and then claim whether there is evidence of a bubble.
Literature review
- Variance bound tests
- West test
- Intristic bubble
- Cointegration tests
- MTAR unit root test
- Switching regime tests
- Unobserved variable
- Mathematical definition based model
- Recursive unit root tests
Cochrane (1992) later tested the existence of bubbles using the variance of the price/dividend ratio. They studied the order of integration of stock prices and dividends in the NASDAQ index. Another difference of the GSADF is in the way the bubble originates and ends.
Model and specification test
The PWY test
The PWY test is based on repeated estimates of the 3.3 from a forward expanding sample set and the test is obtained as the sup value of the corresponding ADF statistical set. In recursion this is the window size of the regression and runs from r0 to 1, where is 3.2. The ADF statistic is calculated recursively from each regression and the sup ADF statistic is then used to detect the presence of a bubble.
They defined the origin date of the bubble as the smallest value of r r0,1 for which ADFris is greater than the critical value.
The PSY test
Rejecting the unit root hypothesis in favor of explosive behavior requires that the test statistic exceed the right-tailed critical value from the marginal distribution. Phillips, Shi, and Yu (2011) derived marginal distributions for the GSADF statistic, which is a nonlinear function.
Date stamping methodology
The bubble end date would be calculated as the first observation after log(. When the BSADF statistic exceeds the finite sample critical values of the SADF, the empirical evidence suggests that the time series exhibits explosive behavior. Since the distributions of the SADF( )r0 and GSADF( )r0 are non-standard; critical values must be obtained via Monte Carlo simulations.
Data
Technical details
The calculation of the SADF statistic, GSADF statistic and the corresponding finite critical values was performed in the Matlab programming environment. There were assumptions about the ADF equation, the delay length and the minimum window size. The ADF equation was assumed to have a constant but not a trend, as the graph of the returns of the data used showed no upward trend and the mean did not return to zero.
The partial autocorrelation of the returns has shown that most information is described in two to four lags for all countries. The ADF computed with fixed four lag length and not using an information criterion because the computational cost would be high despite the results being more accurate. In particular, all data sets were assumed to be 22, which means five years and 2 months, since the total observations for each country are 136.
The sizing window should not be too small to avoid miscalculations, but also not too large, as this would lead to incorrect results. This methodology is quite sensitive to window size; the more it is increased, the more the critical values are reduced and can then cause more exuberant episodes.
Empirical evidence
Figure 2 presents the evolution of the quarterly time series for the ratio of nominal housing prices to rent from the first quarter of 1971 to the third quarter of 2013 with the baseline of the first quarter of 1971. Figure 3 presents the evolution of the time series quarterly for the nominal ratio of house prices to income from the line of the first quarter of 1980 to the third quarter of 2013 since no previous data were available and with the first quarter of 1980 as the base. Spain is again the first to have the largest housing price to income ratio, and this time the United Kingdom follows again, but with Denmark at the same levels.
In Table 2, the comparisons of the SAW and GSAW statistics with the corresponding critical values for the three data sets are set aside. It appears that the dating of bubble signals fits well with the periods when there was a strong rise in real house prices. The nominal house price to rent ratio data set shows a bubble between 2000Q4 to 2004Q3 which also coincides with the first data set, but captures a shorter time period and again the BSADF methodology serves as an early bubble indicator.
According to Taipalus (2006), methodology indicates three periods as bubbles by examining the price-to-rent ratio which coincides with the results of the price-to-rent ratio of this study, but with only small spots of the total period capture The housing price-to-income ratio follows the same path as the housing price-to-rent ratio, which means that the rent and the income in Germany follow the same direction. It appears that the dating of the bubble signals dates well with the periods when real house prices experience a strong increase.
The BSADF technique shows explosive behavior in the first quarter of 2003 through the second quarter of 2004, which coincides with the first data set, but with a shorter duration. The ratio of house prices to rental prices appears to move in tandem with real house prices. The price-rent ratio shows explosive behavior from the second quarter of 1994 to the second quarter of 1997 and a bubble from the third quarter of 2003 to the first quarter of 2006, which almost coincides with the first data set.
Comparison of the empirical results
Dallas Fed International House Price Database of. real house prices ratio prices/rent prices/income ratio. In Figure 28 there is a comparison between the findings of this analysis and those of Pavlidis, et al. 2013) regarding the real house price index for the countries Spain, Finland, Denmark, Italy, UK, France, Germany and the US. Particularly in Spain, Denmark and Great Britain, the date stamp of the bubbles is close to this analysis with Pavlidis, et al. 2013), but in this analysis much earlier warnings of the bubble burst are given.
2013) found a bubble characteristic, whereas in this analysis there was no evidence of explosive behavior. In Figure 29 there is a summary of the findings of the investigation of the countries that were common and use data of the price-to-rent ratio from 1990 to 2014 in research. Although in this case the database used was the same, there are important differences attributed to the significant difference of the size window which is not much more than the Pavlidis, et al.
A critical review indicates much earlier warning signs of this analysis in contrast to other authors. Chen and Funke (2013), who used a maximum-minimum window, their findings seem to capture longer periods and delay the collapse warning. Engsted, Hviid, and Pederse (2015), who have almost twice the smallest window as this analysis, have their results closer to early warning, but there are some disagreements, especially in the case of Germany.
Finally, in Figure 30 there is an overview of the results of the study of the countries that were common between this analysis and Pavlidis, et al.
Conclusion
In this case a different database was used, but the results are not much different. There is agreement that there is no explosive behavior in Finland, but in Italy the results are very different. Overall, this thesis provides earlier warning indicators in all cases, at least one year.
The most important decision regarding this methodology was the determination of the minimum recursive rolling sample size window. Empirically it was found that the more the minimum size window increases, the smaller the critical values will be, so the captured explosiveness will be greater. Furthermore, the synthesis of real housing prices, nominal price-rent ratios and price-to-income ratios is collected by national institutes with different metrics making the data less representative and less comparable.
In this analysis, the results show that in the period from mid-1995 to 2006, there was a sharp increase in all three data sets for all countries included in the research except for Germany and Finland. The BSADF method, which is used for the date-stamping technique of the bubble episodes, reveals explosive behavior in almost all countries. In a comparison with other studies, the results are in most cases about the same, but this analysis presents much earlier warnings that the bubble is bursting.
So it is concluded that this state-of-the-art tool can provide early warning indicators, but the reliability of the exact dating depends firstly on the database that will be used and secondly on the assumptions that will be made.
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