ANÁLISIS COMPARATIVO SEGÚN EL SUBTIPO DE AIJ

Estimation of a repeat-sales index requires several methodological choices. I use transactions data for single-family houses and owner-occupied apartments from 1994 to 2010, a total of 539,452 transactions. I follow convention in the literature and exclude non arm-length transactions, transactions with short holding period, outliers in sales prices and outliers in house price growth, as they may not be representative of market prices.16 _{Specifically, I}

exclude trades between family members, sales due to divorce and death, sales-pair with a holding period of less than 2 quarters, sales where the property is transacted multiple times per year, and the top and bottom 1 percent of sales price and price growth.17 _{Table 8 in}

the appendix shows the details of the sample selection.

The equation of interest is equation (6), and its sample equivalent:

log Pt+τ,i Pt,i = τi X t=1

γtDt,i+ωt,i for all properties i= 1, . . . , n (7)

whereωt,i is an error term, andDt,i equals −1, 0 or 1 depending on whether the property in

16_{Non arm-length transactions are typically not sold at market prices, and a short holding period may}

be because professional house buyers renovate the property with the intention to re-sell it at a higher price. Additionally, a distressed sale may occur due to job loss or divorce.

period t is traded for the first time, not traded, or traded for the second time, respectively. The time dimension is quarterly. Under the assumption thatωt,i has zero mean and constant

variance, equation (7) can be estimated with OLS, and the exponentiated coefficient of γt

is interpreted as the quality-adjusted price index.18 _{Case and Shiller (1987) suggest that}

observations with a long time between sales should be given less weight in the estimation as the error term is likely related to the length of time between transactions. I use the following method to down-weight observations. First, I estimate equation (6) by OLS to obtain the vector of regression residuals. Second, I run a regression of the squared residuals on a constant term and the time interval between sales. Third, I re-estimate equation (6) where each observation is weighted by the square root of the fitted value for the second step.19

The main disadvantage of the repeat-sales methodology is that it discards a large fraction of all observations, as only properties traded twice or more are included (Gatzlaff and Haurin, 1997; Clapp et al., 1991; Jiang et al., 2015). In other words, while the methodology avoids a specification-bias, it may introduce a sample selection bias, as properties traded repeatedly may not be representative of the entire market. Table 1 provide summary statistics on observed characteristics for single transactions and repeat sale transactions, and t-test for the difference between single and repeat sales.20 _{There are 539,452 properties transacted}

two times or more during the sample period, and 267,318 transactions where the property was sold only once. The average square meter price for single-sale (repeat-sales) transactions is 9,018 DKK (9,686 DKK), the average size is 127 (109) square meters and the average property age is 51 (56) years. There is a statistically significant difference between single- and repeat-sales for all three categories.

Even with these differences however, the repeat-sales index remains the most appropriate methodology to use for this study. To see why, consider the alternative estimation methods.

18_{For more details and a practical guide to different house price indexes, see Balk et al. (2013).}

19_{A robustness check confirms that the results are similar if do not down-weight observation based on}

time between sales.

20_{The equivalent table when the sample is split between single-family houses and owner-occupied apart-}

One alternative is the hedonic house price methodology, which uses a bundle of property characteristics and their associated prices to derive a price index. This methodology re- quires a correctly specified functional forms for each characteristic, an inherently difficult proposition. Shiller (2008) argues that a repeat sales index is the “only way to go”, as there are too many different permutations of hedonic data that could possibly allow the researcher to chose their own results. Another alternative is the appraisal-based methodology, which uses data from appraisals (normally tax appraisals) to calculate an index. Tax values are generally available for all properties, which makes this methodology attractive. Indeed, the official property index available from Denmark Statistics is constructed with the appraisal- based method. However, the appraisal-based index relies on having a good assessment of property values. High quality on-site value assessments in Denmark was conducted annually by SKAT prior to 2002. After the freeze of nominal property tax values in 2002 the appraisal is no longer conducted on-site, and housing values are instead estimated from a model of housing transactions. This likely lowers the quality of the appraisal, and therefore limits the attractiveness of the index. Appendix C compares the estimated repeat-sales indices with the official Denmark Statistics property indices, and find a strong level of correspondence between the two different approaches prior to 2002, but also finds that there are increasing differences between the two methodologies after the on-site assessment was abolished in 2002.

Due to the dependency on quality of assessments and to the inherent difficulty in speci- fying a functional form for a hedonic index, I chose to construct a repeat-sales index. With the repeat-sales index, there is no dependence on assessments, and there is no specification bias. As the repeat-sales methodology is prominently used in the United States, this also enables an easier comparison to US house price indices.

5 Results

This section describes the Danish housing market from 1996 to 2010, with a focus on house price developments on a municipal level. There is considerable variation across locations

in both the timing and the amplitude of house price growth. In fact, the geographical clustering, the difference in timing and the difference in amplitude during this period are reminiscent of what Sinai (2013) and Abel and Deitz (2010) document for the US housing market between 1980 and 2010. Further, Danish house prices display the type of short-run momentum and long-run mean reversion that Glaeser et al. (2014) and Head et al. (2014) document for the United States.