**5. Comparative Empirical Analysis**

**5.1. Hodrick-Prescott Filter**

**5.1.2. Empirical Testing**

Before we can go forth with applying the HP filter we must conclude which smoothing parameter we will use for 𝜆. As stated above, Hodrick and Prescott concluded in their paper that a smoothing parameter of 1600 would give the best fit for their quarterly data. Our analysis considers annual data; therefore, we must take this into consideration. The annual data we have collected for our analysis goes back to 1819.

One of the reasons for why we have chosen to look so far back, rather than only looking from 1980 and out is to pick up the historical development. Also, another positive side of having so many data points is that we are able to eliminate some of the end-point problems that occur with the HP filter, at least from the start point. It will be difficult to properly analyze the current situation; however, we will be able to analyze previous bubbles and see whether the model fits or not. If previous bubbles are captured, then we can write about the results with higher confidence.

There are many aspects to think about before choosing the value for 𝜆. A level of 100 has been considered
for annual data (Hodrick & Prescott, 1997). The recent development in the Norwegian housing market
may pose a challenge for having a low 𝜆 since the trend will follow the current extreme values, which in
turn will underestimate a potential bubble. Another problem is highlighted by the European Central
Bank, “the smoothing parameter does not only effect the cycle but the volatility of trend growth and well
*– a consequence of the fact that the HP filter does not contain an explicit model of the cycle.” (ECB, p. *

9, 2005). This is why many economists argue to use high values for 𝜆 when analyzing annual data, because they feel that when using lower values, it would give rise to implausible volatile trend growth rates. Also, using a higher smoothing parameter will ultimately provide more volatility, which also makes a larger portion of the fluctuations a result of temporary disturbances.

To be able to capture both aspects of previous academic conclusions we will use one low and one high smoothing constant. We have chosen to use a newer and an older conclusion of the best fitted value for 𝜆. We will use Ravn and Uhlig’s smoothing parameter for annual data of 6.25 and Correia, Neves, and Rebelo’s smoothing parameter for annual data of 400. Hence, we will be able to see some changes in the results and investigate both sides of the discussion of which value for 𝜆 to use.

Figure 5.1 shows the development of the real house prices for Norway in general and both trend components, using 6.25 and 400 as the smoothing parameter from 1819-2015. When looking at the smoothing parameter of 6.25, the trend moves very close to the real house price, as expected. Therefore, the real house prices only show to be overpriced for a short window in five distinct time periods, which we have already previously have mentioned. That is, the Kristiania Crisis, World War I, the Great

is that the real house prices showed signs of being underpriced at the bottom of the crash. Interestingly enough, if we look at the recent development it actually seems as if real house prices are undervalued.

In 2014, real house prices experienced a minor drop, which is not too surprising considering the recent oil price drop. Here it must be mentioned, that our data only includes data up to 2015, as NCB has not released the most recent data. Therefore, the model does not include 2016’s leap in housing prices.

Figure 5.1

*Source: NCB, 2017; Own calculations*

Next, we look at the smoothing parameter of 400. As the trend becomes more linear with constant growth as 𝜆 increases, it becomes more evident to observe the financial turmoil’s that we have previously mentioned. It becomes clearer that real house prices have been overpriced in these periods, as well as underpriced when the bubbles hit bottom. The gap between the trend and the real house prices during the Norwegian Banking Crisis is the largest gap viewed in our data. After this, the trend seems to have followed the real house prices. Conclusively, given the data we have available, the model indicates that Norway is currently experiencing an underpricing.

The conclusion changes when looking at figure 5.2, which shows the development of the real house prices for Oslo, with both trend components using 6.25 and 400 for 𝜆 from 1841-2015. The data for Oslo looks fairly similar to the data for Norway in general. It could be argued that the data is more volatile in

0 50 100 150 200 250 300 350

1819 1834 1849 1864 1879 1894 1909 1924 1939 1954 1969 1984 1999 2014

### Real house prices with trend lines, Norway (1819-2015)

Real House Prices HP - 6.25 HP - 400

Oslo. Also, the magnitude of the Kristiania Crisis in 1899 is much larger, which is expected as this was primarily experienced in Oslo. The main characteristic we want to point out from this graph is the fact that both trends using smoothing parameters of 6.25 and 400 are below the real house prices from 2014 and out. From this we can conclude that both trends imply that the real house prices in Oslo are overpriced.

Figure 5.2

*Source: NCB, 2017; Own calculations *

We have observed that we currently have two different scenarios in Norway. For Norway in general today’s real house prices are below the estimated HP filters, both when using smoothing parameter’s 𝜆 = 6.25 and 𝜆 = 400, suggesting undervalued prices. However, when looking at Oslo by itself, the real house prices are above the estimated HP filter, which implies overvalued housing prices. From this we can conclude that there could exist a bubble in Oslo, but not for Norway in general.