Abstract
How can a commercial property price index (CPPI) be defined and constructed? And what kind of relationship does the measurement of commercial property’s value have to the System of National Accounts and to concerns about national financial sectors? In order to answer such questions, this paper aims to outline the concepts that can be used to define and measure the value of commercial property, and to clarify the relationship of such measurement to the System of National Accounts and to the financial system.
The base of this chapter is Diewert, W.E. and C. Shimizu. 2019. The system of national accounts and alternative approaches to the construction of commercial property price indexes. Discussion Paper 19–9, Vancouver School of Economics, University of British Columbia. Presented at the 62nd ISI World Statistics Congress, invitation session. Kuala Lumpur, Malaysia, August 19, 2019.
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Notes
- 1.
Note however that there are circumstance where transaction price information is more plentiful than appraisal valuation information, notably in countries (such as the U.S.) where IFRS accounting rules are not yet prevalent, such that assets are normally carried on companies’ books at historical cost rather than at current “fair value.” In the United States, only specialized populations of commercial properties are frequently and professionally appraised.
- 2.
For details of IPD’s real estate investment index, see http://www1.ipd.com/Pages/default.aspx
- 3.
NCREIF: (http://www.ncreif.org/. (Note that the NCREIF Index is based on a little over 7,000 properties, out of a universe of probably some 3,000,000 commercial properties in the U.S.)).
- 4.
http://mitcre.mit.edu/research-publications/cred/transaction-based-index. (Note that the TBI is now produced and published by NCREIF as the “NTBI.”).
- 5.
- 6.
In most cases, the input prices \(w_{tnij}\) will not depend on the particular rented unit i in property n.
- 7.
- 8.
Two important characteristics which are not held constant are the age of the structure and the amount of capital expenditures on the property between the survey dates. Changes in these characteristics are an important determinant of the property price.
- 9.
Another problem with appraisal based indexes is that they tend to be smoother than indexes that are based on market transactions. This can be a problem for real estate investors since the smoothing effect will mask the short term riskiness of real estate investments. However, for statistical agencies, smoothing short term fluctuations will probably not be problematic.
- 10.
The period index t runs from 1 to 44 where period 1 corresponds to Q1 of 2005 and period 44 corresponds to Q4 of 2015.
- 11.
Other papers that have suggested hedonic regression models that lead to additive decompositions of property values into land and structure components include Clapp (1980; 257–258), Bostic et al. (2007; 184), Diewert (2008, 2010), Koev and Santos Silva (2008), de Haan and Diewert (2011), Francke (2008; 167), Rambaldi et al. (2010), Diewert et al. (2011, 2015), Diewert and Shimizu (2015a, b, 2016, 2017, 2019), Burnett-Issacs et al. (2016), Rambaldi et al. (2016) and Diewert et al. (2017).
- 12.
This formulation follows that of Diewert (2008, 2010), de Haan and Diewert (2011), Diewert et al. (2015) and Diewert and Shimizu (2015b, 2016, 2017) in assuming property value is the sum of land and structure components but movements in the price of structures are proportional to an exogenous structure price index. This formulation is designed to be useful for national income accountants who require a decomposition of property value into structure and land components. They also need the structure index which in the hedonic regression model to be consistent with the structure price index they use to construct structure capital stocks. Thus the builder’s model is particularly suited to national accounts purposes; see Schreyer (2001, 2009), Diewert and Shimizu (2015a) and Diewert et al. (2016).
- 13.
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 major repairs to a structure, our age variable will only pick up average gross depreciation less average real renovation expenditures.
- 14.
- 15.
- 16.
For more details on the data and the regressions used in this study, see Diewert and Shimizu (2019).
- 17.
- 18.
Our \(R^{2}\) concept is the square of the correlation coefficient between the dependent variable and the predicted dependent variable.
- 19.
The 23 wards (with the number of observations in brackets) are as follows: 1: Chiyoda (191), 2: Chuo (231), 3: Minato (205), 4: Shinjuku (203), 5: Bunkyo (97), 6: Taito (122), 7: Sumida (74), 8: Koto (49), 9: Shinagawa (69), 10: Meguro (28), 11: Ota (64), 12: Setagaya (67), 13: Shibuya (140), 14: Nakano (39), 15: Suginami (39), 16: Toshima (80), 17: Kita (30), 18: Arakawa (42), 19: Itabashi (35), 20: Nerima (40), 21: Adachi (19), 22: Katsushika (18), 23:Edogawa (25).
- 20.
From this point on, our nonlinear regression models are nested; i.e., we use the coefficient estimates from the previous model as starting values for the subsequent model. Using this nesting procedure is essential to obtaining sensible results from our nonlinear regressions. The nonlinear regressions were estimated using Shazam; see White (2004).
- 21.
The estimated combined ward relative land price parameters turned out to be: \(\omega _{1}=1.3003\); \(\omega _{2}=0.75089\); \(\omega _{3}=0.49573\) and \(\omega _{4}=0.25551\). The sample probabilities of an observation falling in the combined wards were 0.402, 0.278, 0.177 and 0.143 respectively.
- 22.
The sample probabilities of an observation falling in the 7 initial land size groups were: 0.291, 0.234, 0.229, 0.130, 0.050, 0.034 and 0.033.
- 23.
- 24.
Thus \(PS^{t}\) is a normalization of the official construction price series \(p_{St}\) so that \(PS^{t}=1\) when \(t=1\). The series \(PS^{t}\) is plotted in Fig. 5.2.
- 25.
This is land that is usable for purposes other than the direct support of the structure on the land plot. Excess land was first introduced as an explanatory variable in a property hedonic regression model for Tokyo condominium sales by Diewert and Shimizu (2016; 305).
- 26.
The sample probabilities of an observation falling in the 4 excess land size groups were: 0.352, 0.343, 0.149, 0.114 and 0.041.
- 27.
- 28.
It should be pointed out that our estimate for \(\mu \) in our final model is 0.0602 instead of 0.1135.
- 29.
The analysis in this section and the subsequent section follows the approach taken by Diewert et al. (2017). Geltner and Bokhari (2019) estimate a much more flexible model of commercial property depreciation using US transaction data by allowing an age dummy variable for each age of building. This methodological approach generates a combined land and structure depreciation rate whereas our approach will generate depreciation rates that apply only to the structure portion of property value.
- 30.
There were only 28 properties which had age greater than 50 years so these properties were combined with the age 40–50 properties.
- 31.
\(A_{tn}\) is the same as A(t, n). The aging function \(g_{A}(A_{tn})\) quality adjusts a building of age \(A_{tn}\) into a comparable number of units of a new building.
- 32.
Recall that these depreciation rates are net depreciation rates. As surviving structures approach their middle age, renovations become important and thus a decline in the net depreciation rate is plausible. The pattern of depreciation rates is similar to the comparable geometric depreciation rates that were observed for Richmond (a suburb of Vancouver, Canada) detached houses by Diewert et al. (2017).
- 33.
See Diewert and Shimizu (2015b) where these relationships also held for Tokyo detached houses.
- 34.
This does not always happen for straight line depreciation models; i.e., for properties with very old structures, the imputed value of the structure can become negative if the estimated depreciation rate is large enough. This phenomenon cannot occur with geometric depreciation models, which is an advantage of assuming this form of depreciation.
- 35.
Recall that the log likelihood for the comparable geometric model of depreciation, Model 9, was \(-12614.70\) and the \(R^{2}\) for Model 9 was 0.7142. Thus the descriptive power of both models is virtually identical.
- 36.
Recall that these depreciation rates are net depreciation rates. As surviving structures approach their middle age, renovations become important and thus a decline in the net depreciation rate is plausible. The pattern of depreciation rates is similar to the comparable geometric depreciation rates that were observed for Richmond (a suburb of Vancouver, Canada) detached houses by Diewert et al. (2017).
- 37.
The volatility in the raw series could be real phenomenon in that land prices are inherently volatile. If this is the case, it would be useful for statistical offices to publish the unsmoothed series as well as the smoothed series. As noted by Geltner et al. (2014), property investors would find unsmoothed property price indexes useful in order to evaluate the riskiness of property investments. On the other hand, the volatility may be due to the heterogeneity of commercial properties (and the scarcity of market transactions). Thus there are important price determining characteristics of these properties that we have not taken into account in our regressions and this leads to volatility in our indexes.
- 38.
Patrick initially smoothed his series by taking a three month rolling average of the raw index prices for Ireland. He found that the resulting index was still too volatile to publish and he ended up using a double exponential smoothing procedure.
- 39.
The method is due to Cleveland (1979).
- 40.
The initial smoothed series was divided by the Quarter 1 value so that the resulting normalized series equalled 1 in Quarter 1. Recall that Quarter 1 is the first quarter in 2005 and Quarter 44 is the last quarter in 2015.
- 41.
A similar problem of a lack of centering occurred when we implemented the LOWESS smoothing procedure; i.e., we had to divide by a constant to make the first component of the smoothed series equal to one. As a result, the Lowess smooth tended to lie below the raw series as can be seen in Fig. 5.2.
- 42.
A quadratic Henderson type smoother would be much smoother if we lengthened the window. But a longer window would imply a longer revision period before the series would be finalized. Since the linear smoother with window length 5 seems to do a nice job of smoothing, we would not recommend moving to a longer window length for this particular application.
- 43.
The reader may well wonder why we estimated the \(\omega _{n}\) in Model 1 rather than first estimating the \(\alpha _{t}\) in Model 1. When this alternative strategy was implemented, we found that the resulting Model 2 did not converge to the “right” parameter values; i.e., the resulting \(R^{2}\) was very low. This is the reason for following our nested estimation methodology where each successive model uses the final coefficient values from the previous model. It is not possible to simply estimate our final models in one step and obtain sensible results.
- 44.
We also estimated the straight line depreciation model counterpart to Model 3. The resulting estimated straight line depreciation rate \(\delta \) was equal to 0.01317 (t statistic \(=45.73\)). The \(R^{2}\) for this model was 0.9806 and the final log likelihood was \(-13989.83\). The resulting land price series was very similar to the land price series generated by Model 3 above.
- 45.
In the multiple geometric depreciation rate model estimated by Diewert and Shimizu (2017), the various rates averaged out to an annual rate of 2.6% per year. Our earlier study covered the 22 quarters starting at Q1 of 2007 and ending at Q2 of 2012. The correlation coefficient between the price of land series in this model in Diewert and Shimizu (2017) and the above Model 3 price of land series for the overlapping 22 quarters is 0.9901 so these two studies using REIT appraisal data show much the same trends in Tokyo commercial property land prices even though the estimated wear and tear depreciation rates are different. Note that in addition to wear and tear depreciation, depreciation due to the early demolition of a structure before it reaches “normal” retirement age should be taken into account. Our current study does not estimate this extra component of depreciation. However, Diewert and Shimizu (2017) estimated demolition depreciation for Tokyo commercial office buildings at 1.2% per year.
- 46.
The units of measurement used in this section are in 100,000 yen.
- 47.
The sample probabilities of an observation falling in the 5 land size groups were: 0.171, 0.285, 0.175, 0.178 and 0.191.
- 48.
The minimum value for the distance to the nearest subway station \(DS_{tn}\) is 50 meters and the minimum value for the subway running time from the nearest station to the central Tokyo subway station was 4 min.
- 49.
The Laspeyres and Paasche price indexes for quarter t are defined as \(P_{L}^{t}\equiv [PL_{\text {MLIT}}^{t}Q_{L}^{1}+PS_{t} Q_{S}^{1}]/[PL_{\text {MLIT}}^{1}Q_{L}^{1}+PS_{1}Q_{S}^{1}]\) and \(P_{P} ^{t}\equiv [PL_{\text {MLIT}}^{t}Q_{L}^{t}+PS_{t}Q_{S}^{t} ]/[PL_{\text {MLIT}}^{1}Q_{L}^{t}+PS_{1}Q_{S}^{t}]\) respectively. The quarter t Fisher index is defined as \(P_{\text {FMLIT}}^{t}\equiv [P_{L} ^{t}P_{P}^{t}]^{1/2}\) for \(t=1,\ldots ,44\). See Fisher (1922) for additional materials on these indexes. The Fisher index has strong economic and axiomatic justifications; see Diewert (1976, 1992). We also calculated chained Fisher property price indexes using the same data but these indexes were virtually the same as the Fisher fixed base indexes.
- 50.
- 51.
- 52.
Diewert (2010) noticed that the Fisher property price index generated by the builder’s model frequently approximated the traditional log price time dummy property price index using the same data. However, the key to close approximation is that the time dummy model must generate a reasonable implied structure depreciation rate, which is the case for our particular data set.
- 53.
If the age structure of the quarterly sales of properties remains reasonably constant, then this neglect of depreciation will probably not be a factor.
- 54.
These points are well known in the real estate literature; see Chap. 25 in Geltner et al. (2014).
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Diewert, W.E., Nishimura, K.G., Shimizu, C., Watanabe, T. (2020). The System of National Accounts and Alternative Approaches to the Construction of Commercial Property Price Indexes. In: Property Price Index. Advances in Japanese Business and Economics, vol 11. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55942-9_5
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