Abstract
Since real estate is heterogeneous and not all its quality attributes are observable, the repeat sales model pioneered by Bailey et al. (1963) has become one of the standard methods to estimate a constant-quality price index. The model, however, fails to adjust for depreciation, as age and time between sales have an exact linear relationship. This paper proposes a new method to estimate an age-adjusted repeat sales index by decomposing property value into land and structure components. As depreciation is more relevant to the structure than land, the property’s depreciation rate should depend on the relative size of land and structure. The larger the land component, the lower the depreciation rate of the property. This new method is applied to property transactions in Hong Kong and Tokyo. Hong Kong is shown to have a higher depreciation rate based on a fixed structure-to-property value ratio, while the resulting age adjustment is larger in Tokyo because its land value has shrunken over time.
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Notes
Instead of using time dummies, another way is to estimate and predict, through period-by-period hedonic regressions, the value of a reference property over time.
Diewert et al. (2015) proposed a new hedonic model, with construction cost as the additional information, to decompose prices into land and structure components.
In general, the inelastic supply of land makes land value more volatile and more sensitive to economic shocks than building value.
Box-Cox transformation requires that the age variable is strictly positive.
If the error term is suspected to be heteroscedastic, one can apply Case and Shiller’s (1989) Weighted Repeated Sales (WRS) method that allows drift in individual property value through time.
Recruit Co., Ltd. provided us with information on contract prices for about 24% of all listings. Using this information, we were able to confirm that prices in the final week were almost always identical to the contract prices; see Shimizu et al. (2012).
The downward bias in the δ estimate reinforces our prediction that the true δ should be positive.
Shimizu et al. (2010) has described the property attributes used for hedonic estimation, which are not repeated here.
For the hybrid model, Box-Cox transformation has not been applied to the age term and so the depreciation rate is constant (−1.51%).
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Wong, S.K., Chau, K.W., Karato, K. et al. Separating the Age Effect from a Repeat Sales Index: Land and Structure Decomposition. J Real Estate Finan Econ 57, 351–366 (2018). https://doi.org/10.1007/s11146-017-9631-2
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DOI: https://doi.org/10.1007/s11146-017-9631-2