Empirical testing

7.1.3.1 Norway

Real house price index 1980-2015 with HP-filter

Figure 7.1 illustrates the trend line with a lambda value of 100 and 2 500.

Figure 7.1: Time series from 1980-2015 for real house price with HP-filter, Norway (1980=100). Shows lambda value of 100 and 2 500.

As illustrated, there are only short periods where the house prices are overpriced, with a lambda value equal to 100. Hence, the growth in house prices in recent years do subsequently not show signs of a housing bubble. In addition, house prices were underpriced right after the financial crisis.

The real house price index is moving in line with the trend component from 2008, which do not provide any indications of a housing bubble today.

As illustrated, there are greater deviations from the index and trend with a lambda value of 2 500 than it was with a lambda value of 100. The figure illustrates that Norwegian house prices were underpriced in the period between 1990 and 2004. This may be due to the economic recession that happened after the banking crisis in the 1980s. This underlines the HP-filter to be suitable with data where long-term cycles are perceived as a trend, as it distinguishes the time series in trends and cycles.

To further minimize the problems regarding the high growth from the early 1990s, we will now expand the horizon of the time series. This may provide a more correct and valid trend line due to a greater amount of data being included.

Real house price index from 1819-2015 with HP-filter

By extending the analysis back to 1819, we are able to observe earlier crises that have influenced the house price development to a large extent. Additionally, we are reducing the problem regarding long cycles, as the growth since the 1990s becomes a smaller percentage of the total data material in a time series with a longer horizon. We will see whether earlier crises will be evident with apparent deviations between the house price index and the trend.

Figure 7.2: Time series from 1819-2015 for real house price index with HP-filter, Norway (1980=100).

Shows lambda value of 100 and 2 500

As illustrated in figure 7.2, a lambda value of 100 results in small deviations between the index and trend line. There are only a few periods where house prices show signs of being overpriced. The HP-filter still considers the high price growth as a trend rather than an abnormal high growth, and struggles to capture historical bubbles. By using a longer time series, an increase in the lambda value will provide a smoother trend line.

On the contrary, a lambda value of 2 500 clearly illustrates historical bubbles, such as

“Kristianiakrakket”, the postwar period and the banking crisis.

Figure 7.3: Time series from 1819-2015 for real house price index with HP-filter, Norway (1980=100).

Shows lambda value of 2 500

According to the HP-filter with a lambda value equal to 2 500, the Norwegian housing market does not have indications of a housing bubble today. From 2009 to 2013, the trend line was below the house price index, which means that the housing market was overpriced. However, from 2014, the trend line seems to be fairly equal to the house price index. Nevertheless, endpoint problems occur.

We will further illustrate the deviations graphically in order to get a closer look at deviations from trend, as well as differences in the short- and long-term series.

Gaps from the trend line

The figures below show gaps from the house price index and the trend line, with a lambda equal to 2 500.

Figure 7.4: Gap from trend 1980-2015 in Norway. Shows lambda value of 2 500

Figure 7.5: Gap from trend 1819-2015 in Norway. Shows lambda value of 2 500

Both figures (7.4 and 7.5) illustrate the housing bubble in the late 1980s. This resulted in negative deviations, which lasted until 2004. Despite the financial crisis, the model shows positive deviations from 2004 until 2013. From 2014 until today, the deviation is approximately zero, and does not provide any indications of a housing bubble in the Norwegian house market.

Conclusion

The HP-filter with a lambda value of 100 does not provide any indications of a housing bubble, nor with a lambda value of 2 500. However, this result is not highly reliable due to endpoint problems, and since a discretionary aspect is highly involved. This method alone does not provide a conclusive and reliable answer. It will thus be necessary with further analyzes to answer our problem statement.

In section 7.2 we will conduct a supplementary P/R analysis, but firstly we will investigate whether the HP-filter proves the housing bubble in Denmark prior to the financial crisis.

7.1.3.2 Denmark

Real house price index 1992-2015 with HP-filter

Figure 7.6 illustrates that the house price index is far above the trend line with a lambda value equal to 100 between 2004 and 2008.

Figure 7.6: Time series from 1992-2015 for real house price index with HP-filter, Denmark (1992=100).

Shows lambda value of 100.

As illustrated, the figure illustrates that the housing market was overpriced, which corresponds with the fact that there was a bubble in the Danish housing market prior to the financial crisis. However, we have done calculations for a lambda value at 2 500 as well.

Figure 7.7: Time series from 1992-2015 for real house price index with HP-filter, Denmark (1992=100).

Shows lambda value of 100 and 2 500.

Figure 7.7 illustrates the house price index with trends for lambda values of 100 and 2 500. An implementation of a higher value of lambda results in a larger deviation between the price index and the trend line. Both lambda values prove the housing bubble prior to the financial crisis. It is nevertheless important to bear in mind that the HP-filter is more reliable for the Danish housing market as we also have data for the years after the relevant period we are analyzing.

To get a clearer look at the deviations from trend, we will illustrate the gap graphically.

Gap from trend line

The figure below shows gaps from the house price index and the trend line, with a lambda equal to 2 500.

Figure 7.8: Gap from trend 1992-2015 in Denmark. Shows lambda value equal to 2 500.

Figure 7.8 illustrates a bubble, as well as the boom in 2006. This proves that the Danish housing market was experiencing a housing bubble in this period.

Conclusion

The HP-filter for the Danish housing market showed that they experienced a housing bubble prior to the financial crisis. Hence, we believe this model to be valid for the Norwegian house market as well.