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2020 | OriginalPaper | Chapter

4. Estimation of Residential Property Price Index: Methodology and Data Sources

Authors : W. Erwin Diewert, Kiyohiko G. Nishimura, Chihiro Shimizu, Tsutomu Watanabe

Published in: Property Price Index

Publisher: Springer Japan

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Abstract

Fluctuations in real estate prices have substantial impacts on economic activities. In Japan, a sharp rise in real estate prices during the latter half of the 1980s and its decline in the early 1990s led to a decade-long stagnation of the Japanese economy. More recently, a rapid rise in housing prices and its reversal in the United States triggered a global financial crisis. In such circumstances, the development of appropriate indexes that allow one to capture changes in real estate prices with precision is extremely important, not only for policy makers but also for market participants who are looking for the time when housing prices hit bottom. Recent research has focussed on methods of compiling appropriate residential property price indexes. The location, maintenance and the facilities of each house are different from each other in varying degrees, so there are no two houses that are identical in terms of quality. Even if the location and basic structure are the same at two periods of time, the building ages over time and the houses are not identical across time. In other words, it is very difficult to apply the usual matching methodology (where the prices of exactly the same item are compared over time) to housing.

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previous chapter A Comparison of Alternative Approaches to Measuring House Price Inflation

next chapter The System of National Accounts and Alternative Approaches to the Construction of Commercial Property Price Indexes

This chapter–Chap. 7 deal with the following methods: stratification or mix adjustment methods, hedonic regression methods, repeat sales methods, and appraisal based methods.

This decomposition is required in order to construct the national accounts for a country.

The Advisory Board was set up by the Ministry of Land, Infrastructure, Transport and Tourism, with the participation of the Bank of Japan, Financial Services Agency, Ministry of Justice (which is the department responsible for the land registry), Statistics Japan (the department responsible for the consumer price index), the Cabinet Office (the department responsible for SNA), the Japan Association of Real Estate Appraisers and various realtor associations. As of 2013, the Advisory Board also began developing a official Commercial Property Price Index in addition to developing the Residential Property Price Index.

Sections 4.2 and 4.3 draw heavily on the paper by Shimizu et al. (2010a).

See Clapp and Giaccotto (1992). Repeat sales that occur in very short time periods are often not regarded as “ typical” sales. In particular, the initial sale may take place at a below market price and the subsequent rapid resale takes place at the market price, and this phenomenon may lead to an upward bias in the resulting repeat sales price index. Of course, this source of upward bias is partially offset by the downward bias in the repeat sales method due to its neglect to make a quality adjustment for the depreciation of the structure.

See Case and Shiller (1987, 1989), Clapp and Giaccotto (1992, 1998), Goodman and Thibodeau (1998), Case et al. (1991) and Diewert (2010).

See Case and Quigley (1991) and Ekeland et al. (2004).

See Diewert (2003a, b).

See Case et al. (1991), Clapp and Giaccotto (1992, 1998), Shimizu and Nishimura (2006, 2007) and Shimizu et al. (2010a).

See Bourassa et al. (2006). The hedonic method requires information on property characteristics whereas the repeat sales method does not require any characteristics information. However, this informational advantage of the repeat sales method is offset by its informational sparseness disadvantage; i.e., repeat sales information may be so infrequent so as to make the construction of accurate price indexes impossible. Moreover, unless the sample selection bias exactly offsets the depreciation bias, we can say that the repeat sales method is definitely biased whereas we cannot definitely assert that the hedonic method is biased.

This may be partly due to the presence of legal restrictions in Japan on reselling a house within a short period of time.

McMillen (2003) adopted the same Cobb-Douglas production function for housing services. Thorsnes (1997) described housing output as a constant elasticity substitution production function of the lot size and housing capital, and provided some empirical evidence that the elasticity of substitution is close to unity, which implies that the Cobb-Douglas production function is a good approximation of the technology used in the production of housing services. In contrast, Diewert (2010, 2011) suggested some possible hedonic regression models that might lead to additive decompositions of an overall property price into land and structures components. Additive decomposition models have been estimated by Diewert et al. (2011a, b) and Eurostat (2011) using Dutch data and by Diewert and Shimizu (2013) using data for Tokyo. We will discuss these additive models in Sect. 4.5 below.

Note that we are assuming that the vector of house i attributes \(\varvec{x}_{i}\) does not depend on the time of sale, t.

Time dummy hedonic regression models date back to Court (1939).

The repeat sales method is due to Bailey et al. (1963).

Thus the regression model defined by (4.5) does not require characteristics information on the house( except that information on the age of the house at the time of each transaction is required).

However, if s and t are very close, the variance could also increase due to the “flipping phenomenon”; i.e., a house that is sold twice in a short time period may have a rate of price change between the two time periods that is unusually large on an annualized basis, causing the error variance to increase.

As usual, set \(d_{1}^{*}\equiv d_{1}\equiv 1\) so that \(P_{1}\equiv 1\).

Note that the depreciation model defined by (4.2) can be regarded as a net depreciation model; i.e., it is depreciation less “normal” renovation and maintenance expenditures. See Diewert (2011) for more on the topic of constructing a house price index taking depreciation and renovation into consideration.

The analysis which follows is due to Shimizu et al. (2010a).

It should be noted that the official S&P/Case-Shiller home price index is adjusted in the following way to take the age effect into account. Standard and Poor’s (2008: 7) states that “sales pairs are also weighted based on the time interval between the first and second sales. If a sales pair interval is longer, then it is more likely that a house may have experienced physical changes. Sales pairs with longer intervals are, therefore, given less weight than sales pairs with shorter intervals.”

However, one would expect approximate multicollinearity to hold in McMillen’s model so that the estimated dummy variable parameters may not be too reliable.

See Chau et al. (2005) for another example where a nonlinear specification of the age effect was introduced into the hedonic regression in order to eliminate multicollinearity between the age variable and the time dummy variables.

If the estimated \(\lambda \) parameter for the model defined by (4.8) turns out to be close to one, then as is the case for McMillen’s model, there may be an approximate multicollinearity problem with the Shimizu, Nishimura and Watanabe repeat sales model.

The two period time dummy variable hedonic regression was considered explicitly by Court (1939: 109–111) as his hedonic suggestion number two. Griliches (1971: 7) coined the term “adjacent year regression” to describe the two period dummy variable hedonic regression model.

They called their method the Overlapping Period Hedonic Housing Model (OPHM).

This is the approach used by Shimizu et al. (2010a) to form an overall price index. Ivancic et al. (2009) recommended a variant of the rolling window model where their basic hedonic regression model was the Time Product Dummy model which is the application of Summer’s (1973) Country Product Dummy model to the time series context (from the original application to multilateral comparisons of prices across countries). IDF recommended a (weighted) Rolling Year Time Product Dummy method where the window length was chosen to be 13 months. For extensions of the IDF model to more general hedonic regression models, see de Haan and Krsinich (2014). Diewert and Shimizu (2013) implemented a Rolling Window hedonic regression model for Tokyo houses which will be described later in Sect. 4.5. The Rolling Window Hedonic Regression approach to the construction of house price indexes has also been applied by Eurostat (2011; Chap. 8) and by Diewert et al. (2011b).

Shimizu et al. (2004) reported that the Recruit data cover more than 95% of all transactions in the 23 special wards of Tokyo but the coverage for suburban areas is very limited. Therefore the study by Shimizu, Nishimura and Watanabe used only information for the units located in the special wards of Tokyo.

There are two reasons for removal of the listing of a unit from the magazine: a successful deal or a withdrawal; i.e., in the second case, the seller gives up looking for a buyer and thus withdraws the listing. SNW were allowed to access information regarding which of the two reasons applied for individual cases and they discarded prices where the seller withdrew the listing.

Recruit Co. Ltd. provided SNW with information on contract prices for about 24% of the population of listings. Using this information, SNW were able to confirm that prices in the final week were almost always identical to the contract prices; i.e., they differed at less than a 0.1% probability.

More specifically, the imputed land area attributed to a condo unit was calculated by dividing the sum of the floor space for each unit in the structure by \(FAR\times BLR\), where FAR and BLR stand for the floor area ratio and the building to land ratio, respectively. The sum of the floor space of each unit in a structure was available in the original dataset. The maximum values for FAR and BLR are subject to regulation under city planning law. It was assumed that this regulation was binding.

Japanese people are particularly fond of sunshine!

Travel time to the CBD was measured as follows. The metropolitan area of Tokyo is composed of wards and contains a dense railway network. Within this area, SNW chose seven railway or subway stations as central business district stations: Tokyo, Shinagawa, Shibuya, Shinjuku, Ikebukuro, Ueno, and Otemachi. SNW then defined travel time to the CBD as the minutes needed to commute to the nearest of the seven stations in the daytime.

The time to the nearest station, TS, was defined as the walking time to the nearest station if a house was located within walking distance from a station, and the sum of the walking time to a bus stop and the bus travel time from the bus stop to the nearest station if a house is located in a bus transportation area. SNW used a bus dummy, BD, to indicate whether a house was located in walking distance from a railway station or in a bus transportation area.

Note that the estimated coefficient for \(\lambda \) in the age adjusted repeat sales model was 0.89 for condos and 1.10 for single family houses. Thus the exact multicollinearity problem does not arise for these regressions.

Their Rolling Window results used a window length of 12 months and used the updating procedure explained at the end of Sect. 4.2 above.

Note that the age adjusted repeat sales index is well above the other two repeat sales indexes which do not make an adjustment for depreciation of the structure. This result is to be expected. What is perhaps more surprising is that the age adjusted repeat sales index ends up well below the two hedonic indexes. This result may be due to sample selectivity bias in the repeat sales method or to an incorrect specification of the hedonic models.

The annual depreciation rate for houses appears to be much smaller than the corresponding rate for condos and thus the age bias in the repeat sales models will be much smaller for houses than for condos. The relatively large differences in the two hedonic indexes is a bit of a puzzle. Diewert and Shimizu (2013) also compared Rolling Window house price indexes with a corresponding index based on a single time dummy regression and did not find large differences (but the sample period was much shorter in the Diewert and Shimizu study).

It can be seen from the upper right panel of Fig. 4.4 that several dots in the right upper quadrant are well above the 45 degree line, indicating that the growth rates of the standard hedonic index are substantially higher than those of the standard repeat sales index at least for these quarters. These dots correspond to the quarters between 1986 and 1987, during which the standard hedonic index exhibited much more rapid growth than the standard repeat sales index, as was seen in Fig. 4.2.

The material in this section is drawn from Shimizu et al. (2011, 2012). In this section, we will refer to these two papers as SNW.

See for example Case et al. (1991), Diewert (2010), Dorsey et al. (2010), Eurostat (2011) and Sect. 4.2 above. Recently, McMillen and Thorsnes (2006), McMillen (2012) and Deng et al. (2012) proposed a new index estimation method, the matching model method, which focused on the distribution of housing prices.

Eurostat (2011) provides a summary of the sources of price information in various countries. For example, in Bulgaria, Canada, the Czech Republic, Estonia, Ireland, Spain, France, Latvia, Luxembourg, Poland and the USA price data collected by statistical institutes or ministries is used. In Denmark, Lithuania, the Netherlands, Norway, Finland, Hong Kong, Slovenia, Sweden and the UK information gathered for registration or taxation purposes is used. In Belgium, Germany, Greece, France, Italy, Portugal and Slovakia data from real estate agents and associations, research institutes or property consultancies is used. Finally, in Malta, Hungary, Austria and Romania data from newspapers or websites is used.

There are several papers that focused on data sources for housing price indexes; see Gatzlaff and Haurin (1998), Genesove and Mayer (2001), Goetzmann and Peng (2006). However, these papers did not compare multiple data sources.

See Allen and Dare (2004), Haurin et al. (2010), Knight et al. (1998).

See Genesove and Mayer (1997, 2001) and Engelhardt (2003).

An alternative approach would be to compare the four prices in terms of their average prices or in terms of their median prices. However, these summary statistics capture only one aspect of cross-sectional price distributions.

As was noted in the previous section, Shimizu et al. (2010a) constructed five different house price indexes, including hedonic and repeat sales indexes, using Japanese data for 1986 to 2008. They found that there were substantial differences in terms of turning points between hedonic and repeat sales indexes. In particular, the repeat sales measure signaled turning points later than the hedonic measure. For example, the hedonic measure of condominium prices bottomed out at the beginning of 2002, while the corresponding repeat sales measure exhibited a reversal only in the spring of 2004.

See Chapter 11 of Eurostat (2011) for detailed information on house price datasets currently available in Japan.

The number of housing units that appear both in the realtor data set and in the registry data set is 22,613; the number of housing units that are in the realtor data set but not in the registry data set is 99,934; and the number of housing units that are in the registry data set but not in the realtor data set is 36,336.

Eurostat (2011: 147) sums up the situation as follows: “Each source of prices information has its advantages and disadvantages. For example a disadvantage of advertised prices and prices on mortgage applications and approvals is that not all of the prices included end in transactions, and the price may differ from the final negotiated transaction price. But these prices are likely to be available sometime before the final transaction price. Indices that measure the price earlier in the purchase process are able to detect price changes first, but will measure final prices with error because prices can be renegotiated extensively before the deal is finalized.”

DS deleted 9.2% of the observations because they fell outside their range limits for the variables V, L, S, A, NB and W. DS noted that it is risky to estimate hedonic regression models over wide ranges when observations are sparse at the beginning and end of the range of each variable. The a priori range limits for these variables were as follows: \(2\le V\le 20;0.5\le S\le 2.5;1\le A\le 50;2\le NB\le 8;2.5\le W\le 9\).

See Diewert et al. (2011a, b) for evidence on this multicollinearity problem using Dutch data.

The period index t runs from 1 to 44 where period 1 corresponds to Q1 of 2000 and period 44 corresponds to Q4 of 2010.

Other papers that have suggested hedonic regression models that lead to additive decompositions of property values into land and structure components include Clapp (1980), Francke and Vos (2004), Gyourko and Saiz (2004), Bostic et al. (2007), Davis and Heathcote (2007), Francke (2008), Koev et al. (2008), Statistics Portugal (2009), Diewert (2010, 2011), Rambaldi et al. (2010) and Diewert et al. (2011a, b).

This formulation follows that of Diewert (2010, 2011) and Diewert et al. (2011a, b). It is a special case of Clapp’s (1980; 258) hedonic regression model.

This estimate of depreciation is regarded as a net depreciation rate because it is equal to a “ true” gross structure depreciation rate less an average renovations appreciation rate. Since we do not have information on renovations and additions to a structure, our age variable will only pick up average gross depreciation less average real renovation expenditures. Note that we excluded sales of houses from our sample if the age of the structure exceeded 50 years when sold. Very old houses tend to have larger than normal renovation expenditures and thus their inclusion can bias the estimates of the net depreciation rate for younger structures.

See Schwann (1998), Diewert et al. (2011a, b) and Eurostat (2011) on the multicollinearity problem.

All of the \(R^{2}\) reported in this section are equal to the square of the correlation coefficient between the dependent variable in the regression and the corresponding predicted variable. The estimated net annual straight line depreciation rate was \(\delta =1.25\%\), with a T statistic of 17.3.

See Eurostat (2011).

The 21 Wards of Tokyo that had at least one transaction during the DS sample period (with the total number of transactions for that Ward in brackets) are as follows: 1: Minato (69); 2: Shinjuku (136); 3: Bunkyo (82); 4: Taito (15); 5: Sumida (32); 6: Koto (38); 7: Shinagawa (144); 8: Meguro (349); 9: Ota (409); 10: Setagaya (1158); 11: Shibuya (107); 12: Nakano (305); 13: Suginami (773); 14: Toshima (124); 15: Kita (53); 16: Arakawa (34); 17: Itabashi (214); 18: Nerima (925); 19: Adachi (271); 20: Katsushika (143); 21: Edogawa (197). Note that for each observation tn, \(\sum _{j=1}^{21}D_{W,tn,j}=1\); i.e., for each observation tn, the 21 ward dummy variables sum to one.

The annual net depreciation rate for this model was estimated as \(\delta =1.39\%\) with a T statistic of 26.8.

Diewert and Shimizu (2013) estimated several additional models that were generalizations of the model defined by (4.14). These models made use of the NB, WI, TW and TT variables defined above in Sect. 4.5.2. Their final most general Model 5 had an \(R^{2}\) equal to 0.8476 and the corresponding log likelihood was \(-8709.9\).

An alternative way of viewing the land model is that land in each Ward can be regarded as a distinct commodity with its own price and quantity. But since all Ward land prices move proportionally over time, virtually all index number formulae will generate an overall land price series that is proportional to the \(\alpha _{t}\).

Our method for aggregating over different house “ models” that have varying amounts of constant quality land and structures can be viewed as a hedonic imputation method but it can also be viewed as an application of Hicks’ Aggregation Theorem; i.e., if the prices in a group of commodities vary in strict proportion over time, then the factor of proportionality can be taken as the price of the group and the deflated group expenditures will obey the usual properties of a microeconomic commodity. “Thus we have demonstrated mathematically the very important principle, used extensively in the text, that if the prices of a group of goods change in the same proportion, that group of goods behaves just as if it were a single commodity.” Hicks (1946; 312–313).

DS normalized the price indexes \(P_{Lt}\) and \(P_{St}\) to equal 1 in quarter 1, which is quarter 1 of the year 2000.

The Fisher chained index \(P_{t}\) is defined as follows. For \(t=1\), define \(P_{t}\equiv 1\). For \(t>1\), define \(P_{t}\) in terms of \(P_{t-1}\) and \(P_{F,t}\) as \(P_{t}\equiv P_{t-1}P_{F,t}\) where \(P_{F,t}\) is the quarter t Fisher chain link index. The chain link Fisher index for \(t\ge 2\) is defined as \(P_{F,t}\equiv [P_{La,t}P_{Pa,t}]^{1/2}\) where the Laspeyres and Paasche chain link indexes are defined as \(P_{La,t}\equiv [P_{L,t}Q_{L,t-1}+P_{S,t}Q_{S,t-1}]/[P_{L,t-1}Q_{L,t-1}+P_{S,t-1}Q_{S,t-1}]\) and \(P_{Pa,t}\equiv [P_{L,t}Q_{L,t}+P_{S,t}Q_{S,t}]/[P_{L,t-1}Q_{L,t}+P_{S,t-1}Q_{S,t}]\). Diewert (1976, 1992) showed that the Fisher formula had good justifications from both the perspectives of the economic and axiomatic approaches to index number theory.

The mean and median series cannot adjust properly for changes in the relative prices of land and structures or for changes in the average age of the houses sold. Also our mean and median series are for all sales of houses in Tokyo and thus these series were not adjusted for changes in the number of properties sold in expensive wards and less expensive wards. We cannot expect the mean and median series to be very accurate constant quality indexes of house prices; see Eurostat (2011).

The end of sample period price levels range from approximately 0.4 to 0.7. These differences were generated over a period of approximately 30 years so that the small differences in quarterly growth rates eventually cumulate into fairly substantial differences between the indexes.

We note that in order to implement the age adjusted repeat sales model, a form of hedonic regression is required.

In particular, the MLIT data base does not include the age of the structure, which is a key variable. MLIT has therefore constructed a system that collects location related information using Geographic Information Systems or GIS. In addition, a system was established for real estate appraisers to survey detailed characteristics.

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Title: Estimation of Residential Property Price Index: Methodology and Data Sources
Authors: W. Erwin Diewert
Kiyohiko G. Nishimura
Chihiro Shimizu
Tsutomu Watanabe
Publisher: Springer Japan
Book: Property Price Index
Print ISBN: 978-4-431-55940-5

Electronic ISBN: 978-4-431-55942-9

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-4-431-55942-9_4