This document summarizes an approach to constructing commercial property price indexes for Tokyo using three methods: an accounting-based index, a repeat sales index, and time-dummy hedonic indexes. It also describes constructing separate indexes for the land and structure components. The accounting-based approach estimates capital stocks using assessed values. The time-dummy hedonic models include variables for land, structure, age, and fixed effects. Results show the age parameter is positive and no-fixed effects models do not adjust for quality. Separate land and structure indexes are constructed using a geometric depreciation model and one allowing depreciation to vary with age. Issues for further research include justifying the capital expenditures depreciation rate and handling early

1. Alternative Approaches to Commercial Property
Price Indexes for Tokyo
W.Erwin Diewert and Chihiro Shimizu
Discussant: Alicia N. Rambaldi

2. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Outline
1 Overview
2 Overall Price Index
3 Components Indexes
4 Further Issues
5 Coments
A. N. Rambaldi CPPI

3. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overview
Construct overall commercial property price indexes.
Three approaches:
An accounting based index
A "repeat sales" type of index
Time-dummy hedonic type of indexes
Construct indexes for the structure and land components.
Objective: Construct industry balance sheets and measure TFP of
commercial buildings
Accounting based index
Time-Dummy Hedonic modelling based approach:
1 Geometric model of structure depreciation
2 Geometric depreciation that changes with age
Adding the components provides an overall price index
A. N. Rambaldi CPPI

4. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Commercial Property Data Available
Do not sell often. In this study assessed value is used. Thus, the
data set is a complete panel.
Tokyo dataset: 22 quarters, 50 buildings (Real Estate Income Trusts
-REITs).
Other available data: net operating income, property taxes, rentable
floor space, number of basement floors, number of above ground
floors, distance to Tokyo main station.
A. N. Rambaldi CPPI

5. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
A. N. Rambaldi CPPI

6. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
A. N. Rambaldi CPPI

7. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
A. N. Rambaldi CPPI

8. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
Land: VLtn = PLtnLn; n = 1, . . . , 50
A. N. Rambaldi CPPI

9. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
Land: VLtn = PLtnLn; n = 1, . . . , 50
Structure: VLtn = PSt
⇥
0.3Sn(1 − !S )Atn
⇤
;
PSt = construction price index for Tokyo;
0.3 is cost of a SqMt of new commercial property in millions of Yen;
!S = 0.005 quarterly depreciation rate
A. N. Rambaldi CPPI

10. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
Land: VLtn = PLtnLn; n = 1, . . . , 50
Structure: VLtn = PSt
⇥
0.3Sn(1 − !S )Atn
⇤
;
PSt = construction price index for Tokyo;
0.3 is cost of a SqMt of new commercial property in millions of Yen;
!S = 0.005 quarterly depreciation rate
Capital Expenditures: VCEtn = PStQCEtn
QCEtn = [(1 − !CE )QCE,t−1,n] + real average CEtn; t = 2, . . . , 22
Starting Stock = depreciated investment for 5 years; !CE = 0.10
A. N. Rambaldi CPPI

11. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
Land: VLtn = PLtnLn; n = 1, . . . , 50
Structure: VLtn = PSt
⇥
0.3Sn(1 − !S )Atn
⇤
;
PSt = construction price index for Tokyo;
0.3 is cost of a SqMt of new commercial property in millions of Yen;
!S = 0.005 quarterly depreciation rate
Capital Expenditures: VCEtn = PStQCEtn
QCEtn = [(1 − !CE )QCE,t−1,n] + real average CEtn; t = 2, . . . , 22
Starting Stock = depreciated investment for 5 years; !CE = 0.10
Solve for the price of land
A. N. Rambaldi CPPI

12. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Index - P
A national income accounting approach: Construct capital stock estimates by
deflating investments and then adding up depreciated real investments made in
prior periods.
Vtn = VLtn + VStn + VCEtn
Value = Price ⇥ Quantity
Land: VLtn = PLtnLn; n = 1, . . . , 50
Structure: VLtn = PSt
⇥
0.3Sn(1 − !S )Atn
⇤
;
PSt = construction price index for Tokyo;
0.3 is cost of a SqMt of new commercial property in millions of Yen;
!S = 0.005 quarterly depreciation rate
Capital Expenditures: VCEtn = PStQCEtn
QCEtn = [(1 − !CE )QCE,t−1,n] + real average CEtn; t = 2, . . . , 22
Starting Stock = depreciated investment for 5 years; !CE = 0.10
Solve for the price of land
Construct overall chained Fisher price index by forming aggregate price and
quantity for each quarter, P
A. N. Rambaldi CPPI

13. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Overall Price Indexes - PA,P1,P2,P3
A "repeat Psales" type of index - Asset Value Price Index (a Lowe index):
50
Pt
A =
n=1 Vtn P50
n=1 V1n
cannot identify the depreciation, assumes constant quality
Time-dummy hedonic type of indexes
No fixed effects
lnVtn = ↵t + " ln Ltn + # ln Stn + $Atn + ✏tn; Pt
1 = exp(ˆ↵t )
with fixed dummy effects and age
lnVtn = ↵t + !n + $Atn + ✏tn; Pt
2 = exp(ˆ↵t )
only dummy effects (a type of CPD)
lnVtn = ↵t + !n + ✏tn; Pt
3 = exp(ˆ↵t )
A. N. Rambaldi CPPI

14. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Results
Parameter of age is positive (P1, P2)
No quality adjustment (PA, P3)
A. N. Rambaldi CPPI

15. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Components Indexes - P4,P5
Builder’s Model of de Haan and Diewert (2011), and Diewert, de Hann and
Hendriks (2014), Diewert and Shimizu (2013)
A. N. Rambaldi CPPI

16. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Components Indexes - P4,P5
tS
Builder’s Model of de Haan and Diewert (2011), and Diewert, de Hann and
Hendriks (2014), Diewert and Shimizu (2013)
Geometric Depreciation Econometric ⇥
⇤Model
V⇤ = Vtn − VCEtn = "PSn
e
Atn tn + ↵t!nLtn + ✏tn; setting = 0.3
V⇤ St =
P50
n=1
⇢
0.3PtS
Sn
h
e ˆiAtn
+ VCEtn
; V⇤ Lt =
P50
n=1 {ˆ↵t ˆ!nLn}
A. N. Rambaldi CPPI

17. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Components Indexes - P4,P5
tS
Builder’s Model of de Haan and Diewert (2011), and Diewert, de Hann and
Hendriks (2014), Diewert and Shimizu (2013)
Geometric Depreciation Econometric ⇥
⇤Model
V⇤ = Vtn − VCEtn = PSn
e
Atn tn + ↵t!nLtn + ✏tn; setting = 0.3
V⇤ St =
P50
n=1
⇢
0.3PtS
Sn
h
e ˆiAtn
+ VCEtn
; V⇤ Lt =
P50
n=1 {ˆ↵t ˆ!nLn}
Can compute P⇤Lt = ˆ↵t, aggregate structure quantity (including capital
expenditures), aggreate land quantity for t
Form a chained Fisher price index for the aggregate, Pt
4
A. N. Rambaldi CPPI

18. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Components Indexes - P4,P5
tS
Builder’s Model of de Haan and Diewert (2011), and Diewert, de Hann and
Hendriks (2014), Diewert and Shimizu (2013)
Geometric Depreciation Econometric ⇥
⇤Model
V⇤ = Vtn − VCEtn = PSn
e
Atn tn + ↵t!nLtn + ✏tn; setting = 0.3
V⇤ St =
P50
n=1
⇢
0.3PtS
Sn
h
e ˆiAtn
+ VCEtn
; V⇤ Lt =
P50
n=1 {ˆ↵t ˆ!nLn}
Can compute P⇤Lt = ˆ↵t, aggregate structure quantity (including capital
expenditures), aggreate land quantity for t
Form a chained Fisher price index for the aggregate, Pt
4
Geometric Depreciation Econometric Model interacted with Age
V⇤ tn = Vtn − VCEtn = PtS
Sng(Atn) + ↵t!nLtn + ✏tn; ˆ ⇡ 0.3
A. N. Rambaldi CPPI

19. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Components Indexes - P4,P5
tS
Builder’s Model of de Haan and Diewert (2011), and Diewert, de Hann and
Hendriks (2014), Diewert and Shimizu (2013)
Geometric Depreciation Econometric ⇥
⇤Model
V⇤ = Vtn − VCEtn = PSn
e
Atn tn + ↵t!nLtn + ✏tn; setting = 0.3
V⇤ St =
P50
n=1
⇢
0.3PtS
Sn
h
e ˆiAtn
+ VCEtn
; V⇤ Lt =
P50
n=1 {ˆ↵t ˆ!nLn}
Can compute P⇤Lt = ˆ↵t, aggregate structure quantity (including capital
expenditures), aggreate land quantity for t
Form a chained Fisher price index for the aggregate, Pt
4
Geometric Depreciation Econometric Model interacted with Age
V⇤ tn = Vtn − VCEtn = PtS
Sng(Atn) + ↵t!nLtn + ✏tn; ˆ ⇡ 0.3
g(Atn) is a spline type function with three age brackets, each with its own
depreciation parameter. P⇤Lt = ˆ↵t
Form a chained Fisher price index for the aggregate, Pt
5
A. N. Rambaldi CPPI

20. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Results - I
A. N. Rambaldi CPPI

21. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Results - II
A. N. Rambaldi CPPI

22. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Issues for further research/discussion
CE = 10% per quarter has not been backed by any econometric
work.
how one deals with buildings that are demolished early
Komatsu, Kato and Yashiro collected date of construction and date
of retirement data for reinforced concrete office buildings in Japan
A. N. Rambaldi CPPI

23. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Conditional probabilities of demolition are very small for the first 20 years or so
of building life.
From 20 to 42 years, increase from 1.4% to about 11%; t fluctuate around the
10% level from age 43 to 67.
After age 67, the conditional probabilities of demolition increase rapidly to end
up close to unity at age 75.
A. N. Rambaldi CPPI

24. Overview
Overall Price Index
Components Indexes
Further Issues
Coments
Comments
Constructing an index of price change for commercial buildings is a much
more complicated task than that needed for residential property.
Given the use of assessed values, why only use 50 buildings and not all
buildings in Tokyo?
Accounting based index. Is P higher partly due to the $CE = 10% per
quarter?
How can we combine selling prices with the valuations?
It would be useful to have some indication of how they relate.
Which are the relevant hedonics to predict the value of a commercial
building?
For instance, the rentable floor space would seem to be an obvious
indicator of how valuable the building is
What do professional valuators take into account when producing a
valuation?
Might not matter if all we want to do is decompose the valuation
into the proportion due to land and that due to the structure
A. N. Rambaldi CPPI