Land Prices and Fundamentals*
Koji Nakamura* and Yumi Saita*** Monetary Affairs Department, Bank of Japan**Research and Statistics Department, Bank of Japan

Macro Conference @Keio University, Dec. 1-2, 2007

* Bank of Japan, Working Paper Series 07-E-08 1

0.Outline

Outline1. Motivation
2. Literature on land prices in Japan
3. Introduction of a weighted-average land priceindicator
4. Theory of land value determination
4-1. Discounted Present Value Model
4-2. Factors other than fundamentals

5. Empirical analyses
5-1. Cointegration tests
5-2. Error Correction models

6. Conclusion
21. Motivation

Motivation• Have Japan’s land prices been
moving in line with “fundamentals” inthe past 50 years?
• Are there any factors other than“fundamentals” which have influenced
land prices?

3

2. Literature on land prices in Japan

Literature on land prices in JapanThe existing empirical studies can be subject tosome criticisms.
1.

Land price data is not appropriate.
Official land price index is a simple average, underestimating
actual land price developments.

2.

Models do not strictly follow the theoretical foundation ofasset pricing (Discounted Present Value (DPV) model).
For instance, Idee(1992),Yoshioka(2002), and Imagawa(2002)
do not take into account the expected growth rate of income intheir DPV.

3.
4.

Critical values for a cointegration test are not appropriate.
Demographic developments are not adequately taken
into account.
42. Weighted-average land price indicator

What is a weighted-average land
price indicator?
• Calculated using the price levels as weights for
aggregation of the annual growth rate of eachobservation point.
• Specifically, let Pj,t （j=1…J） denote the land priceof the observation point j at time t, and thechange in the aggregated land price indicator （pt）
at time t is defined as below.
Δ p = ∑ j =1
Jt

P

j , t −1

∑ P
J

j =1

Δp

j ,t

j , t −1

The lower case is the natural logarithm multiplied by 100 in percent,and Δ is the first-difference operator.

53. Weighted-average land price indicator

Comparison of land price indicators
350（ 1980=100 ）SNA Land Value

300

Weighted-Average Land Price Index
Published Land Prices(Official Publication)
Urban Land Price Index

250
200
150
100
50
0
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005
year

Sources: Cabinet Office, “National Accounts”; Ministry of Land, Infrastructure and Transportation“Published Land Prices.” ;Japan Real Estate Institute, “Urban Land Price Index.”

6

4-1. Discounted Present Value Model

Discounted Present Value (DPV)DPV model＝ Value of land prices equals the discounted present
value of future income streams the land users will have.

Yt + E t P t +1
Eq.(1)
Pt =1+ rt,where r = i + τ + RPt

P t : price level of land at time t,
Y t : income (rent) at period t,

τ t : tax rate at period t,
R P t : risk premium (6%)

t

t

t

E t : expectation operator based on theinformation set at period t,
r t : cost of funds at period t,
i t : nominal interest rate7

4-1. Discounted Present Value Model

Discounted Present Value (DPV)-continuedSolving the Eq.(1) forward and excluding the explosive
bubble solutions by assuming static expectation for future
income growth (get) and the cost of funds (rt), eq.(1) canbe rewritten as;

Y
t
Pt =
e
rt − g t

Eq.(2)

8

4-1. Discounted Present Value Model

Components of DPV(1) Real GDP
115
110（1980=100）

105
100
95
90
85

Weighted-Average Land Price Index(Nationwide, All purposes, Real)
Real GDP

80
75
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005
year

Sources: Cabinet Office, “National Accounts”; Ministry of Land, Infrastructure and Transportation,“Published Land Prices.”94-1. Discounted Present Value Model

Components of DPV(2) Interest rate gap
24
22
20
18
16
14
12
10
8
6
4
2
0
-2
-4

(%)
Nominal Long-term Interest Rate (Long-term
Prime Rate)
Expected Nominal Growth Rate
Estimated Nominal Long-term Interest Rate

1957

1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

2001

2005

year

The interest rates during the period of financial regulation are notsupposed to have reflected the demand-supply conditions of theeconomy. → We estimate the effective interest rate given the
expected nominal growth rate.

104-1. Discounted Present Value Model

Components of DPV(2) Interest rate gap –continued• The interest rate gap moves cyclically because of the
myopic expectation of economic growth.
• As a result, the DVP has a cyclical movement.
– The interest rate gap should be constant in the long run.
6（％）
Nominal Long-term Interest Rate Gap

4
2
0
-2
1957

1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

2001

2005
year

11

4-1. Discounted Present Value Model

Components of DPV(3)Land Tax Rates
3.0

(%)

(%)
Effective Tax Rate

2.5
2.0

Official Tax Rate
Ratio of Land Valuation for Taxation to Market Prices

1.5
1.0
0.5
0.0
1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999

100
90
80
70
60
50
40
30
20
10
0

2004
year

Sources: Ministry of Internal Affairs and Communications, “Records of Property Prices,”“Reference on Municipal Taxes”; Cabinet Office, “National Accounts.”••

Municipal property tax, city planning tax, and land price tax are
considered.
The amendment of the tax code in 1993 raised the tax base,leading to an increase in the effective tax rate.
→ A further decline in land prices occurred.

124-2. Factors other than fundamentals

Other factors(1) Demography
Share of working-age
population and land prices

Share of home- and land-owners
(%)

4.650

y = 0.0007x + 4.5981

70
60
50
40
30
20
10

Share of home-owing
households
Share of land-owing
households

0-24 25- 30- 35- 40- 45- 50- 55- 60- 65- 70- 7529 34 39 44 49 54 59 64 69 74
Age

Demand for houses and land are highfor working-population.

Weighted-average land prices（ Natural logarithm ）

80

4.648

2

R = 0.5272

4.646
4.644
4.642
4.640
4.638
4.636
60

65

70

75

Share of working-age population (%)

There is a high positive correlation.
13

4-2. Factors other than fundamentals

Other factors(2) Changes in industrial structure
GDP by industry
0%
year

20%

40%

60%

80%

100%

100

（㎡）

Required land per 1 million
yen of value added
83

80

1970

60

1975

40

1980

20

1985

27
4

5

8

9

0

1990

Services Retail trade Electrical Medical Chemicals
machinery, health careequipment
andsupplies

1995
2000
Agriculture, Mining, Construction
Raw Materials
Processing
Wholesale, Retail and Services
Government and Nonprofit Organizations

MiningChanges in industrial structure such asa trend toward the services economy
has reduced demand for land.
→ structural downward pressure on
14
land prices

4-2. Factors other than fundamentals

Other factors(3) Attitude toward land-holding(1) Is land a more advantageous
asset than deposits and stocks?
(Households)(2) Is holding land moreadvantageous than renting land?
(Corporations)(fiscal year)(fiscal year)

2005

2005

2003

2003

2001

2001

1999

1999

1997

1997

1995

1995

1993

1993
0%

20%
Yes

40%

60%

80%

100%

NeutralNo

Don't know

0%20%
Owning Land

40%

60%

80%

Renting Land

Demand for land as an ASSET started to increase recently.

100%
Others15

5-1. Cointegration tests

Relationship between DPV andactual land values
Test whether the DPV model holds for land
values based on the cointegration analysis.
[Specification 1]

p t = β 0 + β 1Trendt + DPV t + et[Specification 2]

p t = β 0 + β 1Trendt + DPV t + β 2 pop t + e t[Specification 3] p t =β 0 + β 1Trendt + β 2 DPV t + et[Specification 4] p t =β 0 + β 1Trendt + β 2 DPV t + β 3 pop t + et

pt：real land value (in logarithm), Trendt：time trend, DPVt：discounted
present values (in logarithm), popt：production population ratio, et：error term
16

5-1. Cointegration tests

Cointegration test statistics(Six large city areas)
ADF(t-value )p-value
Critical Value

1%
5%
10%

ADF(t-value )p-value
Critical Value

1%
5%
10%

(1)All(2)Residential

Specification Specification Specification Specification
12
3
4Specification Specification Specification Specification
1
2
3
4-3.7780.026-4.158-3.504-3.182-4.0580.043-4.665-3.984-3.648-5.0600.004-4.665-3.984-3.648-5.671
0.002-5.074-4.375-4.028-3.4320.059-4.158-3.504-3.182-3.6640.097-4.665-3.984-3.648-4.6340.011-4.665-3.984-3.648-4.6650.026-5.074-4.375-4.028(3)Commercial(4)Industrial

Specification Specification Specification Specification
12
3
4Specification Specification Specification Specification
1
2
3
4-3.2940.079-4.158-3.504-3.182-3.5520.120-4.665-3.984-3.648-4.5650.013-4.665-3.984-3.648-5.1690.002-5.074-4.375-4.028-4.7450.002-4.158-3.504-3.182-5.206
0.002-4.665-3.984-3.648-4.746
0.008-4.665-3.984-3.648-5.0400.011-5.074-4.375-4.028

Shaded figures indicate that the null hypotheses are rejected with the associated critical values.

175-1. Cointegration tests

Implication of thecointegration-test result• A cointegrating relationship exists between the
DPV and the actual real land value.
– This result implies that land values have been broadly inline with their theoretical values.

• The cointegrating relationship can also be foundwhen the share of the working-age population is
included in the model.
– This result implies that the demographic factor other thanthe NPV can have effects on the land value
determination in the long-run.
18

5-1. Cointegration tests

Cointegration Vector(Six large city areas)
Estimated vectors
1. Residential

1.27～1.50
DPV
Working Age Pop 0.06～0.08-0.04～-0.01
Time trend
2. Commercial

1.56～2.06
DPV
Working Age Pop 0.11～0.14-0.08～-0.03
Time trend195-1. Cointegration tests

Cointegration Vector(Regional area)
Estimated vectors
1. Residential

0.51～1.09
DPV
Working Age Pop 0.04～0.16-0.02～-0.01
Time trend
2. Commercial

0.50～0.95
DPV
Working Age Pop 0.02～0.08-0.06～-0.02
Time trend205-1. Cointegration tests

Theoretical and actual real land
values (Residential)
Six Large City Areas
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0

Regional Area

（Natural Logarithm）

5.0

theoretical（Natural Logarithm）

4.5
①
④ 4.0
③
② 3.5

③
①②
④

3.0
2.5

actual2.0
60 65 70 75 80 85 90 95 00 05
year

60 65 70 75 80 85 90 95 00 05
year• Recently, the theoretical values have been above
the actual real land values.
215-1. Cointegration tests

Theoretical and actual real land
values (Commercial)
Six Large City Areas
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5

Regional Area

（Natural Logarithm）

4.5（Natural Logarithm）

4.0
3.5
①
③
④ 3.0
②
2.5

①②
④
③

2.0
60 65 70 75 80 85 90 95 00 05

60 65 70 75 80 85 90 95 00 05

year

year

• Similar results for commercial area.
• For regional area, there is no cointegrating relationshipbetween the DVP and the actual real land value.
– A model taking account of (a) bank lending and (b) spillover fromthe land value of city area is cointegrated.
22

5-1. Cointegration tests

Interpretation of developments intheoretical land values• The DPV has fluctuated largely owing to thecyclical movement of the interest rate gap.
– The discrepancy between the myopic
growth expectation and the long-term
interest rate has been a source of theevolution of land values.
• Demographic developments affect the land
value determination in the long run.
23

5-2. Error Correction Model

Determinants of the short-termchanges in land values• Estimate an error correction model(ECM) for the changes in land values
using the cointegrating relationship.
Δp t = β 0 + β 1EC t −1 + β 2ΔDPV t + β 3Δpopt + β 4Δct + ε t
Growth rate of the Error Correction
real land values
term

Growth rate of
the DVP

Change in the share Growth rate ofof the working-age the real banklending*1
population*1 the growth rate of the DPV is subtracted from the growth rate of real bank lending.
24

5-2. Error Correction Model

Estimation results of ECM
Six Large City Areas
Residential

Commercial

Industrial

EC(-1)-0.26(0.05) ***-0.25(0.06) ***-0.21(0.05) ***

ΔY
ΔD
ΔC
C
Adj. R-squared
S.E.

0.80
0.02
0.49
-0.04
0.69
0.07

(0.21) ***(0.03)(0.19) **(0.01) ***

0.94
0.13
0.44
-0.05
0.63
0.09

(0.27) ***(0.04) ***(0.25) *(0.02) ***

0.83
0.06
0.68
-0.01
0.63
0.08

(0.23) ***(0.03)(0.20) ***(0.02)

Regional Area

Residential

Commercial

Industrial

EC(-1)-0.23(0.09) **-0.28(0.06) ***-0.15(0.06) **

ΔY
ΔD
ΔC
ΔPu

0.87
0.03
0.60

(0.21) ***(0.03)(0.18) ***(0.19) ***(0.03) **(0.18) ***

-0.02
0.49
0.07

(0.13) ***(0.02) **(0.11) ***(0.06) ***(0.01) ***

0.77
0.07
0.69

C
Adj. R-squared
S.E.

0.60
0.05
0.54
0.36
-0.03
0.87
0.04

―
(0.01)

―
-0.03
0.53
0.07

(0.01) **25

5-2. Error Correction Model

Determinants of land price changes(Residential)
Six Large City Areas
50

Regional Area（y/y,％）

30
Bank Lending
Demographic
Discounted Present Value40
30

ＥＣ term
Estimated
Actual20（y/y,％）
Bank Lending
Demographic
Discounted Present Value

25
20

ＥＣ term
Estimated
Actual

15
10

10

5
0

0

-10

-5

-20

-10

-30

-15

-40

-20
1980

1985

1990

1995

2000

2005
year

1980

1985

1990

1995

2000

2005
year

26

5-2. Error Correction Model

Determinants of land price changes(Commercial)
Six Large City Areas
50

Regional Area（y/y,％）

30

40
30
20

Bank Lending
Demographic
Discounted Present Value

25

ＥＣ term
Estimated
Actual15（y/y,％）
Land price of six large city areas
Bank Lending
Demographic
Discounted Present Value
ＥＣ term
Estimated
Actual

20

10

10

5

0

0

-10

-5

-20

-10

-30

-15

-40

-20
1980

1985

1990

1995

2000

2005
year

1980

1985

1990

1995

2000

2005
year

27

6. Conclusion

Conclusion
1.

2.
3.

There are cointegrating relationships between the realland values and the discounted present values of land.
• This relationship resulted from cyclicalmovements of the interest rate gap based on the
myopic growth expectations.
The demographic factors have significant impacts onland values even in the long run.
The recent recovery of land values has been brought
about by• Upturn in economic fundamentals under the lowinterest rate environment,• Convergence with the theoretical land values,• Halt in the decline in bank lending.
28

Remarks

Remarks
How do we consider “Bubble”?
1. Myopic expectation:“Expectation Bubble”
2. Discrepancies between estimated land
values and actual land values:“Temporary Bubble”
29