Bank of Japan Working Paper Series

Land Prices and Fundamentals

Koji Nakamura*kouji.nakamura@boj.or.jp

Yumi Saita**
yumi.saita@boj.or.jp

No.07-E-8
April 2007

Bank of Japan
2-1-1 Nihonbashi Hongoku-cho, Chuo-ku, Tokyo 103-8660*

Research and Statistics Department**

Research and Statistics Department

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Land Prices and Fundamentals

Koji Nakamura*, Yumi Saita**
April 2007
Abstract
This paper examines the long-term relationship between macro economic fundamentals
and the weighted-average land price indicators, which are supposed to be more
appropriate than the official land price indicators when analyzing their impacts on themacro economy. In many cases, we find the cointegrating relationships between theweighted-average land price indicators and the discounted present value of landcalculated based on the macro economic fundamentals indicators. We also find that thedemographic factor has impacts on real land prices. The error-correction analysis using
the cointegrating relationships shows that not only the changes in the discounted present
value of land, but also the changes in the demographic factor and bank lending have an
influence on the fluctuations of real land prices. Based on the analysis, the recentchange in the trend of land prices in Japan is explained by the increase in the discounted
present values of land in the accommodative monetary environment, the convergence of
the actual land prices to the long-term equilibrium level, and the changes in banklending.
Key words: weighted-average land price indicators, discounted present value of land, cointegration
analysis, error-correction model
JEL Classification: C32, E39* Research and Statistics Department (E-mail:kouji.nakamura@boj.or.jp)**Research and Statistics Department (E-mail:yumi.saita@boj.or.jp)

We would like to thank Kiyohiko Nishimura, Yoichi Matsubayashi, Naohito Abe, Toshitaka Sekine, Hideo
Hayakawa, Eiji Maeda, Takeshi Kimura, Masahiro Higo, and many staff members at the Bank of Japan for helpfulcomments and discussions. We are grateful to Chie Arai for her research assistance. Any remaining errors belong to
the authors. The views expressed in this paper are those of the authors and do not necessarily reflect those of the
Bank of Japan or the Research and Statistics Department.

11. Introduction
The surge in land prices in the mid 1980s induced the increase in speculative landtransactions and bank lending. After that, we saw a plunge in land prices, which in turnhas caused an increase in non-performing loans and the destabilization of the Japanesefinancial system. During this process, commentators and economists had argued
whether there were “bubbles” in land prices, how large the bubbles were in the mid
1980s, and what the appropriate levels of land prices were in line with economic
fundamentals. There seems to be a consensus so far that the levels of land prices in themid 1980s cannot be explained by economic fundamentals and that there were bubbles
in land prices.1 The criteria of the analysis and the degrees of the impact of the land
price bubble vary, however. Recently, there seems to be changes in the trend of land
prices after the long-time stagnation. Some economists suggest that the recent change inthe land price trend reflect the recovery in the real economy, while others claim that theexcessive monetary easing has contributed to the resurgence in land bubbles.
Given the above arguments in the past, this paper will provide a basis tomeasure whether the actual land prices are in line with fundamentals or not. Specifically,
this paper will examine: (a) how much the discounted present values of land are, basedon the economic fundamentals; (b) whether the demographic and other factors haveaffected the land price fluctuations; and (c) how much the land prices should be once
taking into account of those factors in (a) and (b). In this paper, we use “the weightedaverage land price indicators,” which are supposed to be the appropriate land priceindicators when comparing with other macro economic indicators. We use theweighted-average land price indicators for the cointegration and error-correction
analyses. Compared with the past cointegration analyses on Japanese land prices, thispaper is unique in using: (a) the weighted-average land price indicators, and not theofficial land price indicators; (b) the long-term time series data over 50 years; and (c)the discounted present values of land in line with theoretical formation of land prices.
The conclusions are summarized as follows. First, in many specifications, wefind the cointegrating relationships between the real land price indicators and thediscounted present values of land calculated by using the real GDP, interest rates, theexpected growth rates of the GDP, tax rates, and risk premiums. We also find that thedemographic factor has impacts on land prices in many cointegration specifications.
Second, we find that the error-correction models using the identified
cointegrating relationship fit the short-run fluctuations of the real land prices very well.
1

The comprehensive studies on land prices during the bubble period include Bank of Japan (1990),
Iwata (1992), Nishimura (1995 a), Yoshikawa (1996, 2004), and Uemura and Sato (2000).
2

These error-correction models include not only the discounted present values of land,
but also bank lending and the changes in the demographic factor. Based on theerror-correction model analyses, we identify the following factors contributing the surge
in land prices during the mid 1980s: (a) the myopic expectations that the high nominal
GDP growth would continue with the low interest rate environment: (b) bank lending;and (c) error terms, which are not explained by the models.
Third, the error-correction models show that the recent turnaround of land pricetrends is attributable to: (a) the error-correction of the actual land prices to the long-term
equilibrium levels of land; (b) the sustainable growth in the GDP with the continued low
interest rate environment; and (c) the downward trend in bank lending coming to a halt.
The paper is organized as follows. In section 2, we look into land priceindicators in Japan in detail. In section 3, we overview the theory of land pricedetermination. In section 4, we survey previous empirical researches on Japanese land
prices. In section 5, we test the cointegrating relationship and estimate theerror-correction models. Finally, section 6 provides conclusions and some remarks on
the bubbles in land prices.

2．Land Price Indicators in Japan
In this section, we will look into how the official Japanese land prices indicators areconstructed and what modifications are needed when analyzing them in comparison
with other macro economic indicators. We, then, discuss other important issues for theempirical researches on land prices.
(1) Issues on Construction of Land Price Indicators
Representative land price indicators in Japan are the Urban Land Price Index by theJapan Real Estate Institute and the Published Land Prices by the Ministry of Land,
Infrastructure and Transportation. They aggregate annual growth rates of each checkpoints with equal weights. Therefore, the weights are the same in high valued land priceareas and low valued land price areas. In the past, large fluctuations had occurred in thehigh valued land price areas. If we used the official land price indicators, we would
underestimate the impact of land price fluctuations for high land price areas such as theTokyo metropolitan area. While specialists of land price evaluation carefully investigate
whether each check point is representative for the area’s land price trend, the number ofobservation points does not match the relative importance of each point in terms of land
values. Therefore, when analyzing land price fluctuations with macro economic3

indicators such as the GDP and bank lending, it is appropriate to use different weights inaggregating the annual growth rates of each survey point.
To address this weight issue, we calculate the weighted-average land priceindicators and use them for this paper’s analysis.2 The weighted-average land priceindicators are calculated using the price levels as weights for aggregation of the annual
growth rate of each observation point. P jt （j=1…J） is the land price level of time t ofthe observation point j, and P t is the aggregate land price index level. Δ p t is theannual growth rate of the aggregate land price index calculated as follows.
Δ p = ∑ j =1
Jt

P

j , t −1

∑ P
J

j =1

Δp .
j ,t

(1)

j , t −1

The lower case is the natural logarithm multiplied by 100 in percent, and Δ is thedifference operator.
The different weights are used for each year’s aggregation, and therefore theweighted-average land price indicators are the chain-weight price indexes. By doing this,we can eliminate the bias coming from simple aggregation in the official land priceindicators, and compile the appropriate land price indicators for macro economic
analysis.3 The movements of the weighted-average land price indicators are very muchin line with the anecdotal evidences during the bubble period and the fluctuations of the
SNA land values (Figure 1).4 On the other hand, the official land price indicators suchas the Urban Land Price Index and Published Land Prices showed a gradual increaseduring the bubble period, and this suggests that those indicators underestimated theactual surge in land prices at that time.

2

Details of the weighted-average land price indicators are described in Saita et al. (2004), Bank ofJapan (2006). Saita et al. (2004) used the values (=square measures ×unit prices), not prices as
weights for aggregation. After checking the developments of square measures of several areas,
however, there were some outliers. Therefore, the Bank of Japan (2006) and this paper use prices as
the alternative weights as the second best choice. A detailed discussion on this issue is in footnote 5of Saita et al. (2006).
3
A detailed discussion on the comparison of the weighted-average land price indicators and otherland price indicators is described in appendix 1.
4However, the trend of land values of SNA diverged from that of the weighted-average land priceindicators since the mid 1990s. Particularly, the divergence is significant in local areas where theweighted-average land prices declined while the land values of the SNA increased during the period.
Appendix 1 looks into this issue in detail.
4

(Figure 1) Long-Term Trends of Land Price Indicators5
350（1980=100）
SNA Land Value
Weighted-Average Land Price Index
Published Land Prices(Official Publication)
Urban Land Price Index

300
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.”(2) Issues on Transaction Prices and Evaluation Prices of Land
Real-estate appraisers evaluate the land of the observation points, and their evaluations
are used for the Urban Land Price Index and Published Land Price Index. Theseevaluated prices may differ from the actual transaction prices. In the case of the
Published Land Index, real-estate appraisers evaluate land based on either (a) the
discounted present value evaluation of the land, or (b) transaction prices nearby theobservation points. As Nishimura (1995b) pointed out, this kind of land evaluation isappropriate when land price fluctuations are insignificant. The evaluatedprices ,however, tend to underestimate the actual price fluctuations when the actual land
prices move by a large margin as was the case in the bubble period. In addition, it isessentially difficult to assert that the transaction prices of land represent the actual
trends in land prices since land is not transacted frequently.
This paper will not deal with this issue. In the past, there were some research
papers where land price indicators were constructed by using the actual transaction
prices. Saita (2003) collected auction prices of land in the Tokyo metropolitan area, andconstructed land price indicators with quality adjustments by the hedonic approach. The
Ministry of Land, Infrastructure and Transportation collects land transaction data andhas started to publish them on its web site. While these are very useful to capture the5

The data of Published Land Prices by the Ministry of Land, Infrastructure and Transportation are
observed as of January 1 each year. We treat them as year-end data of the previous year.
5actual trend of land prices, sufficient amounts of time-series data are not accumulated
and therefore, they are not used for the time-series data analysis such as thecointegration analyses.
(3) Issues on Data Frequency
The publication frequency of the official land price indicators is low; the Urban Land
Price Index is published semiannually, and the Published Land Prices are publishedannually lagging a few months behind the observation time. It is, therefore, difficult tocapture the actual situation of prices in real time. Only recently, private-sector
institutions have started to publish high-frequency data of land prices on a quarterly oreven monthly basis with fewer lags.6 However, these data are not sufficient enough to
conduct a time-series data analysis at this point.
This issue may not be problematic for our analysis in this paper. It is possible
to interpolate the annual data by using the spline function to match the data frequency of
the GDP or other economic data. Such modification of the data, however, will notprovide additional information, and the results of the time-series analysis will not bechanged by using such an artificial data series.7(4) Issues on Investigation Period
The fluctuation cycle of land prices are longer than those of other economic indicators.
In the past 50 years after the World War II, Japan experienced 13 business cycles, while
it only has four episodes of land price fluctuations which were in; the early 1960s, early
1970s, late 1970s, and mid 1980s. Existing research on land prices mainly focused on
the land price fluctuation in the mid 1980s and in this case only one episode is includedin the time-series analysis. Such a treatment is not enough to figure out the stable
relationship between land prices and other macro economic indicators.
This paper uses the long-term time series data of land prices in the past 50
years including four episodes of land price fluctuations in Japan. The weighted-averageland price indicators are only available after 1970. We use the Urban Land Price data
before 1969 and connect them to the weighted-average land price indicators.

6

These include “Research on real estate market” by Misawa MRD Inc. and “Residential Land
Prices” by Nomura Estate Urban Net Inc.
7
A more fundamental problem is that we have only a few episodes of land price fluctuations for thelast 50 years. We have no way but to only wait for further accumulation of the land price data in the
future.
6

3．Determinants of Land Prices
In Section 3, we overview the theory of land price determination, that is, the discounted
present value model of land and look into the determinant factors of land prices. We
also check the actual developments of the determinant factors. Furthermore, we
consider whether the factors not taken into account in the standard theory of land pricedetermination could have any impacts on land price fluctuations.
(1) Discounted Present Value Model(Derivation of the Discounted Present Value of Land)
The determinant theory of land prices is the same as that of stock prices; the value ofland is equal to the discounted present value of future income streams the land users
will have as follows;
Y t + E t P t +1 ,
1+ rt

(2)

and r t = i t +τ t + RP t ,

(3)

Pt =

where P t denotes the land price at period t, P t +1 denotes the land price at period t+1, E tdenotes the expectation operator based on the information set at period t, Y t denotes theincome (rent) at period t, r t denotes the cost of funds at period t, i t denotes the nominalinterest rate at period t, τ t denotes the tax rate at period t, and RP t denotes the risk
premium at period t.
Solving the above equation forward, we have the following equation.
h ⎛⎡ ∞ ⎧ h ⎛ 1 ⎞⎫
⎤
1 ⎞
lim
+
∏
Pt = E t ⎢ ∑ ⎨ ∏ ⎜
Y
P
⎬
+
+
t
h
t
h
⎥.
⎟
⎟
h →∞ k = 0 ⎜ 1 +⎝ r t +k ⎠⎣ h=0 ⎩k =0 ⎝ 1 + r t + k ⎠ ⎭⎦(4)In order to exclude the explosive bubble solutions, the second term in equation (4)needs to be zero. Therefore, the land price should be the discounted present value of
future incomes shown as follows:⎡ ∞ ⎧ h ⎛ 1 ⎞⎫⎤Pt = E t ⎢ ∑ ⎨ ∏ ⎜⎬ Y t +h ⎥ .
⎟⎣ h=0 ⎩k =0 ⎝ 1 + r t + k ⎠ ⎭
⎦

7

(5)

Further, we assume; (a) static expectation for future income growth, that is, income willgrow at a constant growth rate ( g te ), and (b) the cost of funds for the future period( r t + k ) is the same as the current one ( r t + k = r t ). Then, the theoretical price of land issimplified as follows;8
Pt =

Yt .
e
rt − gt(6)(Nominal and Real Land Prices)
We did not distinguish the nominal land prices from the real land prices in derivation of
the theoretical land prices above. Here, we consider the difference. In equation (6), we
assume that both the land price and income are nominal. By dividing both sides ofequation (6) by the general price level ( Π t ), let the real land price be p t = P t , the realΠtincome y t = Y t . Then we have the following equation (7). As you see, the numerators
Πtof the both sides are real, but the denominators of both sides are the same as before.
pt =

yt
.
e
rt − gt(7)

When we conduct the time-series analysis in this paper, we use the real GDP as a proxyof real income ( = y t ), and the weighted-average land price indicator denominated by
the GDP deflator as a proxy of the real land price.
(Interest Rate Gap)
Next, we consider the denominator of equation (7). The Fisher identity shows thefollowing relationship;it = qt + π t .
e(8)Here, q t denotes the real interest rate, and π te denotes the expected inflation rate. The
8

In general, expectation for future income growth is strongly affected by the current income growthrate. Such myopic expectation has contributed to the large fluctuations in land prices.
8

expected growth rate of the nominal income is g te and it is decomposed into the expected
growth rate of the real income ( f te ) and the expected inflation rate ( π te ) ;g t = f t + π te .
e

(9)

e

By using the relationship of equation (8) and (9), then the denominator of equation (7)is arranged as follows;

(

)

e
e
i t − g t + τ t + RP t = q t + π t − f t + π t + τ t + RP t = q t − f t + τ t + RP t .
e

e

e

(10)

This means that the nominal discount factor is the same as the real discountfactor. The nominal interest rate in the above equations is considered as the averagevalue of the future short-term interest rates, and therefore it is equivalent to the nominal
long-term interest rate. Excluding the tax rate and the risk premium, the left-hand sideof equation (10) is considered as the “nominal long-term interest rate gap” calculated as
the difference between the nominal long-term interest rate and the expected growth rateof nominal income. The right-hand side of equation (10), on the other hand, is thedifference between the real long-term interest rate and the expected growth rate of thereal income, and can be named as the “real long-term interest rate gap.” Equation (10)shows that the “nominal long-term interest rate gap” is equal to the “real long-term
interest rate gap.”9(2) Developments of Factors of the Discounted Present Value ModelIn this subsection, we look into the developments of determinant factors of the
discounted present value of land.
(Real GDP and Real Land Prices)
The numerator of the discounted present value model is the real income obtained fromthe land owned. When analyzing land prices in terms of the macro economy, the real
GDP is used as a proxy of real income. This is because the appropriate indicators of real
income from land are not available. This is appropriate when we assume that the income
share of land users is constant over time.
9

We assume that the term structure of future inflation expectations reflected in the long-term
nominal interest rate is the same as that reflected in the expected growth rate of the nominal income.
9The long-term time series data of the real GDP and real land prices show thefollowing developments. The growth rates of real land prices are much higher thanthose of the real GDP until the first half of the 1970s when Japan experienced
exceptionally high growth and the Plan for Remodeling the Japanese Archipelago was
implemented. In the mid 1970s, real land prices declined to the same level of the real
GDP and both increased moderately until the first half of the 1980s. During the bubble
period since the mid 1980s, real land prices surged much faster than the real GDP. Afterthe burst of the bubble in the early 1990s, real land prices started to decline while thereal GDP grew steadily. In the mid 1990s, real land prices declined to the same level as
the real GDP. Real land prices, however, continued to decline after that.
This paper analyzes not only the nationwide land prices, but also the regional
land prices. Therefore, we use the real income data of prefectures in addition to thenationwide real GDP data.10(Figure 2) Real GDP and Real Land Price Indicator11
115
110
105
100
95
90
85
80
75

（1980=100）

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

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.”(Interest Rate Gap)
Figure 3 shows the nominal interest rate gap, which is the difference between thenominal long-term interest rate12 and the expected growth rate of the nominal GDP.13
10

We do not estimate the factor income for each usage of land since such an estimate is difficult.
Therefore, the parameters of the cointegrating regressions show the degree of the elasticity of realland prices to the overall real income of the region or nationwide. Since the prefecture income data
are available until fiscal 2003, we estimate the income data of 2004 and 2005 by using effective job
offers data.
11
The real GDP and the real land price indicator are in the natural logarithm.
12
The long-term prime rate of bank lending is used.
13
The expected growth rate of the nominal GDP is the growth rate of the quarterly nominal GDP
10

The nominal interest gap has an obvious inverse correlation with the output gap; when
the nominal interest gap increases, the output gap declines (Figure 3).
(Figure 3) Nominal Interest Rate Gap and Output Gap
6

(%)

4
2
0
-2
-4
Nominal Long-term Interest
Rate Gap
Output Gap

-6
-8
-10
-12

1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005
year

Such a relationship, however, has been observed only after the Japanesefinancial market was liberalized in the early 1980s. Before the early 1980s, the Japanesefinancial market was heavily regulated and interest rates were controlled by theauthorities. Therefore, the demand-supply conditions of the economy were not reflectedin the movements in the nominal long-term interest rates. The data shows that (a) thelevels of the long-term interest rate gap before the early 1980s are different from thoseafter the mid 1980s, and (b) the cyclical movements of the nominal long-term interest
rate gap before the liberalization of the financial market are much larger than those after
the liberalization. In this paper, we estimate the nominal long-term interest rate gap
consistent with the economic development during the regulation and use it forcalculation of the discounted present value of land.14(Tax Rate and Land Prices)
Since various taxes are levied on possessions and transactions of land, the changes inthe tax system have affected land prices. This paper explicitly takes into account the
impact of tax rate changes of land possessions since they can be easily estimated.
There are three taxes: (a) municipal property tax; (b) city planning tax; and (c)land price tax. The land price tax was introduced in 1991 to curb the surge in land prices.
filtered by Hodrick-Prescott filter (λ＝100). Usually, λ＝1,600 is chosen for quarterly data. We,
however, find that the survey data (“Survey on Corporate Activities” by the Cabinet Office) showthat the filtered series of λ＝100 match with the expected growth rates of nominal income.
14
Appendix 2 shows how to estimate the nominal long-term interest rate gap.
11

It, however, was suspended in 1998 since land prices continued to decline. On the other
hand, the official tax rates of property tax and city planning tax have been constant since1978. The official evaluation rates15 of land for the property tax were around 20 percentof the market prices until the early 1990s. Therefore, the effective tax rates of landpossessions were stable, about 0.5 percent of the market prices. Since there was a strong
view that the large difference between the tax base of land and market prices should benarrowed, the authorities amended the tax code in 1993 to raise the tax base so as tomatch market prices. The increase in the tax base of land led to the hike in the effective
tax rate of land holding and induced a further decline in land prices (Figure 4).
Municipal governments, however, had introduced measures to alleviate such an abrupt
hike in the effective tax rates such as special tax exemptions. Thanks to these measures,the actual increase in the effective tax rates was fairly moderate. The effective tax rateof land holding based on the actual tax amount increased moderately since 1991. We use
the effective tax rate based on the actual tax amount paid by tax payers when we
calculate the discounted present value of land.16,17(Figure 4) Land Tax Rates
3.0
2.5
2.0

(%)

(%)
Effective Tax Rate
Official Tax Rate
Ratio of Land Valuation for Taxation to Market Prices (Right scale)

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.”

The impacts of tax rate changes of land transactions, such as transfers,
acquisitions, and inheritances, are difficult to measure since the actual tax amounts vary15

It is the share of the official evaluation value of land to the current market value of land.
The effective tax rates are available until fiscal 2004. We assume that the effective tax rate is thesame in 2005 and use it for the present value calculation.
17
Mera et al. (1992) describes the role of land holding tax on land prices in detail.
1612due to; (a) the difference in the transaction amounts and capital gains, and (b) the
different tax rates and tax deductions calculated together with the other incomes. This
paper, therefore, gives up estimating the impacts of those transaction tax rates on land
prices. The estimation residuals are assumed to contain such impacts.
We, however, could make qualitative assessments of the impacts of the landtransaction tax rates as follows. First, it is suggested that the income tax rate on capitalgain of land transactions induced a delay in sales of lands since the tax rate on the
short-term holdings of lands was higher than that of long-term holdings. This effect, theso called “lock-in effect,” was particularly strong during the bubble period since many
land owners expected a further surge in land prices and larger capital gains. This led to afurther tightening of the land market, a decline in land sales, and an increase in landdemand, as evidenced in the transaction numbers declining during the bubble period
especially in the Tokyo metropolitan area (Figure 5).
(Figure 5) Number of Land Transactions
160
140
120
100
80
60
40
20
0

（1970＝100）

Tokyo
Tokyo metropolitan area(*)
Nationwide
1970

1975

1980

1985

1990

1995

2000

2005
year

Note(*): Tokyo metropolitan area includes Tokyo, Kanagawa, Chiba and Saitama.
Source: Ministry of Justice, “Monthly Report.”

Second, the inheritance motivation increased land demand during the bubble
period. The effective tax rate of inheritance of land is lower than that of financial assets,
and such a tendency became stronger during the bubble period since the market pricesof land were much higher than the evaluation prices. The turnaround of land prices
inversely affected land prices. Such impacts will be captured in the fluctuations ofestimated residuals.
(Risk Premiums)
Next, we consider risk premiums. It is assumed that the risk premium in the long term is

13

constant, while the risk premium in the short term fluctuates sharply reflecting
investors’ risk tolerance. In this paper, we assume that the risk premium is constant andthe constant risk premium is used for calculating the discounted present value of land.
When we use such a discounted present value of land and estimate land prices, theresiduals should contain the variable part of the risk premium fluctuating in the shortterm. If the variable risk premium moves procyclically with business cycles, land prices
move much more than the discounted present value of land.
We use the constant risk premium of six percent in this paper based on paststudies. Using actual land price data, Fujiwara and Shinke (2003) estimated the variablerisk premium, which fluctuates from about one to seven percent, and on average about
six percent. Their estimation result of six percent is consistent with our assumption inthis paper. The risk premium of six percent is also consistent to the risk premium
observed in the stock market in the United States18 (Kocherlakota (1996)).
(3) Other Factors Affecting Land Prices
Based on the discounted present value model, land prices are determined by the income
level, the expected growth of future income, interest rates, tax rates, and risk premiums.
There are, however, other factors affecting land prices. In this subsection, we review
such factors; i.e. demographics, industrial structure, bank lending, and motive for a storeof value.
(Demographics and Land Prices)
How does the demographic factor affect land prices? The simplest idea is that, if thecountry’s territory is constant, the increase in population leads to the rise in demand forland. If a particular cohort of the population has a preference for land and residential
assets, then the changes in the demographic structure, not necessarily coinciding withthat in the total population, can change the demand for land. A survey shows that theacquisition of land and houses is only limited to the cohort from ages 15 to 65 years old,and in the cohort of population aged over 65 years old, the share of land and house
holding remains unchanged (Figure 6).19
18

It is difficult to judge whether the risk premium of land is higher or not than that of stocks. In
terms of liquidity and transaction costs, stocks are assumed to have lower risk premiums. In Japan,
however, land has been long been indentified to be a superior asset than stocks, and in this regard
stocks are not necessarily advantageous assets, and therefore the risk premium of stocks may or may
not be higher than that of land.
19This does not necessarily mean that population aged over 65 years old never purchase land andhouses. In fact, there is a trend that these people, who used to live in the suburban areas around theTokyo metropolitan area, are now moving into the downtown area by selling their own houses in the14(Figure 6) Share of House and Land Owners (2003)
80

(%)

70
60
50
40
30

Share of home-owing households

20

Share of land-owing households

10
0
-24

25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74

75Age

Source: Ministry of Internal Affairs and Communications, “Housing and Land Survey, 2003.”

Demand for houses and land are high, when the share of the population aged 15-64 is high (Figure 7). Even for commercial real estate properties, there are someconcerns for the future deterioration of the market condition due to the aging
population.
(Figure 7) Population Share: Aged 15-64 and Over 65
70

(%)

(%)

25

68

20

66

15

64

10
Share of working-age population
Share of elderly population (right scale)

62

5
0

60
1955

1960 19651970

1975 1980 1985

1990 1995 2000

2005
year

Sources: Ministry of Internal Affairs and Communications, “Population Estimates,” “Report on
Internal Migration in Japan.”

Demand for land comes from demand for services of land-use. Based on thesuburban areas.
15

theory of land price determination, this means that the increase in demand for land-use
leads to the increase in rent, the numerator of the discounted present value equation. If
the rent is accurately measured and is reflected in the land prices, the changes in the
demographic structure should be reflected only through the changes in rent.
Usually, the GDP is used for a proxy for rent when analyzing land prices interms of macro economic analysis. As mentioned earlier, the income distribution shareof land to GDP is assumed to be constant over time. The GDP, however, changes due
not only to the changes in demand for land, but also to other factors. Therefore, when
we analyze land prices using the GDP as a proxy for rent, we may not capture thechanges in demand for land due to the demographic changes. In this regard, we need toconsider the possibility that the demographic changes may have impacts on land prices
not through the changes in the GDP. Furthermore, since the supply of land is inelastic ina short-term period, the surge in demand for land in a short time period tends to lead toan abrupt increase in land prices. Taking this possibility into account, we conduct aquantitative analysis including the demographic factor.
The municipal data show that (a) there is a positive correlation between theshare of the population aged 15-64 and land prices, and (b) there is a negative
correlation between the population aged over 65 and land prices (Figures 8 and 9).
(Figure 8) Population Aged 15-64
and Land Prices(Figure 9) Population Aged over 65
and Land Prices

4.650

4.650

4.648

2

R = 0.5272

Weighted-average land prices（Natural logarithm）

Weighted-average land prices（ Natural logarithm）

y = 0.0007x + 4.5981

4.646
4.644
4.642
4.640
4.638

y = -0.0006x + 4.6525

4.648

2

R = 0.3849
4.646
4.644
4.642
4.640
4.638

4.636
60

65

70

4.636

75

10

Share of w orking-age population (%)

15
20
25
Share of elderly population (%)

30

Time series data show that (a) there is a positive correlation between the population
aged 15-64 and land prices (Figure 10), and (b) the pace of increase in land prices tends
to be slower as the share of the elderly population rises (Figure 11).

16

(Figure 10) Share of Population Aged
15-64 and Land Prices

4.660

1989

4.650

Weighted-average land prices（Natural logarithm）

Weighted-average land prices（Natural logarithm）

4.660(Figure 11) Share of Population Agedover 65

2005

4.640

1978

4.630

1968
4.620
4.610

1989

4.650

2005
1972

4.640
4.630
4.620
4.610
4.600

4.600
60

62

64

66

68

70

72

Share of w orking-age population (%)

0

5
10
15
20
Share of elderly population (%)

25

In this paper, we use the share of people aged 15-64 to the total population as a proxy
for the demographic factor when we conduct quantitative analysis since the correlation
between them seems to be most robust.20
Mankiw and Weil (1988) initiated the analysis on the relationship between
property prices and the demographic factor. They estimated the demand for housing ofeach age cohort and conducted a quantitative analysis on whether the changes indemographics had impacts on housing prices. They found that the share of the
population aged 15-64 was an important determinant of housing prices, and predictedthat housing prices would decrease due to the declining share of the cohort in the 1990s.
Contrary to their prediction, housing prices during the 1990s soared in the United States.
Martin (2005) analyzed housing prices by the general equilibrium framework, andfound that the declines in the long-term interest rate during the 1990s had contributed tothe increase in housing prices. Otake and Shintani (1996) analyzed housing prices inJapan using the same research strategy as Mankiw and Weil (1988). They found that thedemographic factor had impacts on housing prices in the short run, but not in the longrun due to the flexible supply of housing. Iwata and Hattori (2003), on the other hand,claimed that the aging population had an impact on the land value to GDP ratio since
the workforce population declines and the time preference of households increases
based on the basic growth model analysis.
20

The share of the population aged over 65 shows the trend increase (Figure 7). The cointegration
analysis later in this paper includes equations with the trend term, which may capture the impact of
the increase in the elderly people. The trend term, however, may reflect other structural changes suchas the increase in land supply and the change in the industrial structure.
17

As shown above, research results vary on whether the change in demographics
has impacts on property prices such as land and housing prices. In this paper, we willconduct a quantitative analysis with and without the demographic factor in the
cointegration analysis and include the demographic changes in the error-correction
analysis.
(Changes in Industrial Structure and Land Demand)
Next, we consider the changes in the industrial structure of Japan and their impacts onland demand. After World War II, Japan started rebuilding its economy from heavy
industry such as steel and chemical industries. Then, the machinery industry increased
its share in Japan. Later, the service industry has become the major industry in Japan(Chart 12).
(Figure 12) Changes in Industrial Structure
Agriculture, Mining, Construction

Raw Materials

Processing

Wholesale, Retail and Services

Government and Nonprofit Organizations

year

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1970
1975
1980
1985
1990
1995
2000

Source: Ministry of Land, Infrastructure and Transportation, “White Paper on Land, 2006.”

Such structural changes in industries may have had impacts on land demand.
The required land area producing value added of one million yen is 83 ㎡ for the steel
industry, but is only 5 ㎡ for the retail and service industries (Figure 13).

18

(Figure 13) Required Land per One Million Yen of Value Added
100
80
60
40
20
0

（㎡）

83

4

5

8

9

Services

Retail trade

Electricalmachinery,equipment andsupplies

Medical health
care

27

Chemicals

MiningSources: Ministry of Land, Infrastructure and Transportation, “Survey on Land Purchases by Firms”;
Ministry of Finance, “Financial Statements Statistics of Corporations by Industry, FY2003,
2004.”The increasing share of the service industry in the Japanese economy has
possibly induced the declining trend in land demand. Therefore, this change may haveexerted downward pressure on land prices in Japan. Such an impact will be captured by
the trend term in the cointegration analysis. Furthermore, many manufacturing firms
have been actively investing in overseas with the backdrop of globalization. Such atrend may have a negative impact on land prices in Japan.
(Bank Lending and Changes in Land Prices)
It has been pointed out that there is a close correlation between bank lending and land
prices in addition to the impact through the interest rate channel. It is conceivable that(a) the changes in land prices cause the changes in bank lending, and (b) bank lending
provokes the changes in land prices. With regard to (a), the changes in land prices cause
the changes in the collateral value of bank lending, leading to the fluctuations in banklending21. With regard to (b), banks provide financing to firms, which are actively
engaged in speculative land transactions, encouraging further fluctuations in land prices.
In the real world, both mechanisms work. It would be appropriate, however, to consider
that such an impact may not have long-term impacts on land prices. As seen before, thetheoretical value of land is determined by income levels, interest rates, and thedemographic factor together with tax rates and risk premiums. In this regard, bank21

Firms will possibly make more investments when they feel that financing conditions become
accommodative as collateral values increase with the surge in land prices. The mechanism, however,
implies that the declines in land prices will put further downward pressure on the economy when theeconomy is in a recession. Changes in the collateral value of land, therefore, can destabilize theeconomy. Kiyotaki and Moore (1997) analyzed this mechanism with the general equilibrium
framework and called this mechanism “financial accelerator.”
19

lending is not supposed to be a factor to have impacts on land prices in the long-term
period. In the following quantitative analysis, we exclude bank lending in the
cointegration analysis, but include it in the error-correction analysis for the short-run
fluctuation.22(Land Demand as Store of Value)
The notion that land prices should be determined based on their discounted present
value of land comes from the idea that the fundamental value of land is future rents. The
benefit that the land owners have by holding land is equivalent to what they would haveby renting land. This means that there is no unique benefit by holding land. However,there may be demand for land as a store of value, which does not necessarily correspondto the value of using lands. In 1993, a survey on households shows that more than 60
percent of households regard land to be a more favorable asset than financial assets suchas deposits and stocks (Figure 14(1)). In addition, firms also think that holding land ismore advantageous than renting land (Figure 14 (2)).
(Figure 14) Attitude toward Land-holding(1) Is land a more advantageous asset(2) Is holding land more advantageousthan deposits and stocks?

than renting land?

(Households)(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%
Owing Land

40%

60%
Renting Land

80%

100%

Others

Sources: Ministry of Land, Infrastructure and Transportation, “White Paper on Land, 2006,” “Surveyof land ownership and usage by corporations, 2005.”
22

The later analysis shows, however, that commercial land in the local areas is affected by banklending even in the long-term period.
20

The share of which land is more advantageous declined as land prices decreased andrecorded its lowest level in fiscal 2002 and 2003. The share, however, reversed when
the trend in land prices changed recently. Such demand for land as a store of value
cannot be captured by the original land price determination theory, and therefore thismay be obtained in the estimated residuals.

4．Literature on Empirical Research on Japanese Land Prices
In this section, we review the previous empirical analysis on Japanese land prices. This
paper is unique with the following features: (a) data used for the cointegration analysis;(b) specifications of estimation models and explanatory variables; (c) critical values ofcointegration tests; and (d) specifications of error-correction models.
First, this paper uses the different land price data comparing the previous
empirical analyses. The previous empirical studies such as Idee (1992), Yoshioka (2002),
and Imagawa (2002) used the Urban Land Price Indexes as the macro land priceindicators. As described in detail in section 2, the Urban Land Price Indexes may not beappropriate land price indicators since they are the simple sum average of the changes inland prices, and therefore they tend to underestimate the actual fluctuations of land
prices. The weighted-average land price indicators used in this paper correct such a bias
and reflect the actual large fluctuations in land prices.
Second, this paper is unique in specifications of the estimation of thecointegrating regressions and the explanatory variables. The previous studies such as
Idee (1992) used the estimation equation (11) as follows. This specification is different
from the original theoretical land price specification in that (a) the elasticity of land
prices to the real GDP is different from that to the real interest rate, and (b) equation(11) does not take into account the expected growth of future income.
p t = β 0 + β 1 y t + β 2r t ,(11)where p t denotes the real land price in the natural logarithm, y t denotes the real GDP
in the natural logarithm, and r t is the real interest rate.
This paper calculates the discounted present values of land first, and thenestimates the cointegrating relationship between them to the real land prices in line withthe original theoretical specification of land prices. Yoshioka (2002) and Imagawa(2002) calculate the “fundamental value,” which is the real GDP denominated by realinterest rate. While this specification is fine with respect to (a), it does not include the21expected growth rate of income23. It would be better to include both interest rates andthe expected growth rate of income for calculation of the fundamental values of land.
There is another problem in choosing interest rates. Before the liberalization of
the financial market in the early 1980s, previous studies used the observed interest rates
when calculating the discounted present values of land. Such a calculation, however, is
problematic since the observed interest rates did not reflect market conditions andeconomic fundamentals. In order to evaluate asset prices such as of land at that time, itis necessary to estimate the interest rates, which would have realized if the financial
market had been liberalized.
Third, we use the appropriate critical values for cointegrating tests. Idee (1992),
for example, used -2.6 as ten percent critical value for the ADF test. It is necessary,
however, to use the critical values provided by MacKinnon (1991) when the
cointegrating vectors are unknown, taking into account (a) the numbers of estimatedvariables, (b) total observations, and (c) inclusion/exclusion of the trend term 24 .
Imagawa (2002) used the critical value of 15 percent for cointegration tests, which israther high.
Fourth, we have the different error-correction model specifications. For
example, Idee (1992) included the level of real interest rates both in the cointegrating
equations and the error-correction equations. If the interest rates are included in the
cointegrating regression in the level, the first difference in the interest rates should be
included in the corresponding error-correction models. The parameter on the interest
rate in the error-correction model is positive, implying that the rise in interest rates leads
to the increase in land prices. This mechanism is contrary to the original theory of land
price determination and the results of the cointegration analysis.
Housing prices, rather than land prices, are investigated in the cointegration
analyses of the United States. While Capozza, Hendershott, Mack, and Mayer (2002),
and Meen (2002) concluded that there were cointegrating relationships between housing
prices and economic fundamentals indicators, Gallin (2003) claimed that there were nocointegrating relationships.
Other than cointegration analyses, there were several empirical analyses on thechanges in land prices. For example, Nishimura (1995a) used the year-on-year changes
in the Urban Land Price Indexes as dependent variables and the differences in the real
GDP growth and changes in real interest rates as independent variables. He estimated
23

Both Yoshioka (2002) and Imagawa (2002) used nominal rather than real indicators.
We used the program for calculation of the critical values and p-values provided by Professor
MacKinnon on his web site (http://qed.econ.queesu.ca/faculty/mackinnon/).
24

22

the equations by ordinary least square, and claimed that, while the fits before 1984 werevery good, the fits of the equations deteriorated considerably once including the data
after 1985. Based on the results, he claimed that there were bubbles in land prices after
1985. The specifications of Nishimura (1995a) are rather ad hoc in terms of thetheoretical foundation of land prices. Based on the theory of land price determination,
the levels of land prices are explained by the real income level divided by the difference
between the expected growth rate of income and interest rates as suggested by equation(7). Alternatively, taking natural logarithm of equation (7) and the difference from theprevious period, the year-on-year growth rate in land prices can be explained by thegrowth rate of income and the change in the natural logarithm of the difference between
the expected growth rate of real income and real interest rates. If cointegrating
relationships are detected, inclusion of such relationships would improve the efficiencyof estimation as an error-correction term. Based on previous studies as mentioned, thispaper uses the estimation specifications in line with the original theory of land pricedetermination.

5．Cointegration and Error-Correction Analysis(1) Unit Root Tests
First, we will check the results of unit root tests for real land prices. The null hypothesisof the existence of unit roots for the indicators’ levels of any purposes and any regions
were not rejected at the 5 percent significance level (Table 1).
(Table 1) Results of Unit Root Tests(1) Real Land Prices
Nationwide
All
Residential
Commercial
Industrial

Six Large City Areas

Local Areas

Level

-2.25

<0.455>-2.85<0.189>-2.32<0.418>

1 difference
Level

-2.95

<0.004> ***-2.63<0.010> ***-3.00<0.003> ***-2.00<0.588>-2.58<0.289>-2.14<0.514>-3.61<0.009> ***-3.18<0.027> **-3.34<0.001> ***-2.38<0.385>-2.86<0.184>-2.09<0.541>-2.63<0.010> ***-2.46<0.015> **-2.74<0.007> ***-2.59<0.286>-3.24<0.090> *-2.85<0.189>-3.05<0.003> ***-2.84<0.006> ***-2.82<0.006> ***stst

1 difference
Level
st

1 difference
Level
st

1 difference23(2) Discounted Present Values of Land
Nationwide

Six Large City Areas

Local Areas

Level

-1.54

<0.799>-1.62<0.767>-1.74<0.719>1 difference-4.94<0.000> ***-5.03<0.001> ***-3.82<0.005> ***st(3) Share of Working-Age Population to the Total Population
Nationwide

Six Large City Areas

Local Areas

Level

-1.74

<0.715>-4.94<0.001> ***-3.03<0.136>

1 difference-3.42<0.016> **-3.94<0.004> ***-3.93<0.019> **st(4) Share of Bank Lending to the Nominal GDP
Nationwide

Six Large City Areas

Local Areas

Level

-1.77

<0.704>-2.20<0.477>-1.37<0.859>1 difference-5.02<0.001> ***-5.16<0.001> ***-5.61<0.000> ***st(Note 1) ADF τ -values are reported above. The values in < > are p-values.
(Note 2) *, **, and *** respectively indicates a rejection of the null hypothesis with 10%, 5%, and
1% significance level.

The unit root tests for the first difference of any indicators suggest that the null
hypotheses of the existence of unit roots were rejected at most 5 percent level.
Therefore, the real land price indicators are I(1).2526
The unit root tests for the discounted present values of land are conducted. The
discounted present values of land ( NPV t ) are calculated using the following equation(12)27. As mentioned before, if we assume that the expected inflation rates are the same
in both the nominal long-term interest rates and the expected growth rate of nominal
income, then the nominal long-term interest rate gaps are the same as the real long-term
interest rate gaps. We, therefore, construct the nominal long-term interest rate gap using
the nominal long-term interest rates and the expected growth rate of nominal income;

NPV t =

yt,i t − g + τ t + RP
e
t

(12)

where y t denotes the real GDP, i t denotes the nominal long-term interest rate,g t denotes the expected growth rate of nominal income, τ t denotes the tax rate, ande

RP denotes the risk premium (= 6 percent).
25

The six large city areas includes prefectures including the six large cities (Tokyo, Yokohama,
Nagoya, Kyoto, Osaka, and Kobe) in Japan; Tokyo, Kanagawa, Aichi, Kyoto, Osaka, Hyogo. The
local areas includes all the other prefectures.
26
We conducted the Dickey-Fuller GLS tests for all indicators and had similar results.
27 For the unit root and cointegration tests, we used three-year moving average of NPV.
24

The unit root tests for the discounted present values of land indicate that these
indicators are I(1). We also have the similar results for other indicators of I(1).
(2) Specifications of the Cointegrating Regressions
We assume the following four specifications of the cointegrating relationship. The
simplest one is that the real land prices are regressed by the discounted present values ofland, constant term and the trend term. In this specification, the trend term can represent
the structural decline in demand for lands due to the changes in the economic structure,
particularly the steady increase of the service industry, and increasing share of theelderly population, and/or the gradual increase in land supply.
Specification 1 assumes that there is one-to-one relationship between real land
prices and the discounted present value of land.
(Specification 1)
p t = β 0 + β 1Trendt + NPV t + e t ,(13)where p t denotes the real land price in the natural logarithm, NPV t denotes thediscounted present value of land in the natural logarithm, Trendt denotes the trend term,e t denotes the estimation residuals.
Specification 2 assumes the one-to-one relationship between real land prices
and the discounted present value of land as in specification 1. Furthermore, specification
2 includes the demographic factor, which is the share of working-age population to thetotal population, assuming that it would have an independent influence on land prices
besides the discounted present value of land.

(Specification 2)
p t = β 0 + β 1Trendt + NPV t + β 2 pop t + et ,(14)

where p t denotes the real land prices in the natural logarithm, Trendt denotes thetrend term, NPV t denotes the discounted present value of land in the natural logarithm,
pop t denotes the share of working-age population to the total population in the natural

logarithm, and e t denotes the estimation residuals.
Specification 3 relaxes the restriction on the coefficient of the discounted
present value of land of one. The coefficients are estimated by OLS using equation (15)
as follows.

25

(Specification 3)
p t = β 0 + β 1Trendt + β 2 NPV t + et

(15)

Finally, specification 4 assumes that the coefficients of the discounted present
value of land are estimated by OLS and includes the demographic factor.
(Specification 4)
p t = β 0 + β 1Trendt + β 2 NPV t + β 3 pop t + et

(16)(3) Critical Values of the Cointegration Tests
We use the Engle-Granger (1987) method for cointegration tests, that is, first we
estimate the above equations (13), (14), (15), and (16), and then conduct the unit root
tests for estimation residuals ( eˆt ).28 It is not appropriate, however, to use the criticalvalues for one-variable unit root test. In this regard, we use critical values forcointegration tests proposed by MacKinnon (1991), taking into account; (a) sample size,(b) numbers of cointegrating vectors, and (c) existence of the constant and trend terms.
It is rare to have large sample size more than 100 observations for macro economic
indicators. Therefore, we need to use the critical values with small sample proprieties as
MacKinnon (1991) provided.
For specification 1 and 2, we conduct the cointegration tests as follows.
(a) Calculate the series x t = p t − NPV t , the difference between the real land prices andthe discounted present value of land.
(b) For specification 1, conduct the usual unit root test for x t with the constant andtrend terms.
(c) For specification 2, estimate the cointegrating regression with x t as a dependent
variable and the demographic factor, the constant term and the trend term as
independent variables. Use the estimated residuals for the cointegration tests withthe appropriate critical values provided by MacKinnon (1991).

28

The cointegration test proposed by Johansen (1988) is also popular. Johansen (1988) assumes that
all of the cointegrating vectors are endogenous variables. For the analysis on land prices, thediscounted present values of land and changes in demographics are supposed to be exogenous toland price fluctuations, therefore we use the Engle-Granger procedure here.
26

(4) Results of Cointegration Tests
The results of the cointegration tests are reported as follows.
(Nationwide)(Table 2) Results of Cointegration Tests

ADF(t-value)
p-value1%

Ｃritical Ｖalue

5%
10%

ADF(t-value)
p-value1%

Ｃritical Ｖalue

5%10%(1)All(2)Residential

Specification Specification Specification Specification
12
3
4Specification Specification Specification Specification
1
2
3
4

-2.69
0.245
-4.171-3.511-3.186-3.38
0.163-4.665-3.984-3.648-3.52
0.127-4.665-3.984-3.648-3.45
0.263-5.074-4.375-4.028-2.80
0.204-4.171-3.511-3.186-3.93
0.056-4.665-3.984-3.648-4.00
0.048-4.665-3.984-3.648-5.05
0.011-5.074-4.375-4.028(3)Commercial(4)Industrial

Specification Specification Specification Specification
12
3
4Specification Specification Specification Specification
1
2
3
4

-2.43
0.360
-4.171-3.511-3.186-2.97
0.311-4.665-3.984-3.648-3.25
0.204-4.665-3.984-3.648-3.14
0.396-5.074-4.375-4.028-4.35
0.006-4.171-3.511-3.186-4.32
0.023-4.665-3.984-3.648-4.66
0.010-4.665-3.984-3.648-5.71
0.002-5.074-4.375-4.028(Note) Shaded figures indicate that the null hypotheses are rejected with the associated criticalvalues.

The null hypotheses of no cointegration are not rejected fornationwide-commercial land with at most 10 percent level of significance. This result
suggests that the land price determination of the local areas, particularly commercial
lands, is different from those of other regions and usages. For residential lands, the null
hypothesis was rejected at 5 percent level in the specification 3 and 4. For industrial
lands, the null hypotheses are rejected at 1 percent level in the specification 1, and 5
percent level in the specification 2, 3 and 4.

27

(Six Large City Areas)
Next, we conduct the cointegration analyses for the regional data with four
specifications as in nationwide. The results for the six large city areas are as follows(Table 3).
(Table 3) Results of Cointegration Tests for the 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(Note) Shaded figures indicate that the null hypotheses are rejected with the associated criticalvalues.

The null hypotheses of no-cointegration are rejected at 5 percent level ofsignificance in the specification 1 and 2, and at 1 percent level in the specification 3 and4 on the data of all use of lands. The null hypotheses are rejected at 10 percent level inthe specification 1 and 2, and at 5 percent in the specification 3 and 4 on the data ofresidential lands. On the data of commercial lands, the null hypotheses are rejected at 10
percent level in the specification 1, 5 percent in the specification 3, and 1 percent in thespecification 4. Finally, the cointegration test results for industrial lands show that thenull hypotheses are rejected at 1 percent level in the specification 1, 2, and 3, and at 5
percent in the specification 4.

28

(Local Areas)
The results of the cointegration analysis for the local areas are reported as follows(Table 4).
(Table 4) Results of Cointegration Analysis (Local 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
12
3
4-2.8300.194-4.158-3.504-3.182-3.1680.232-4.665-3.984-3.648-3.0040.296-4.665-3.984-3.648-3.412
0.278-5.074-4.375-4.028-3.5370.047-4.158-3.504-3.182-5.347
0.002-4.665-3.984-3.648-3.8140.072-4.665-3.984-3.648-5.602
0.003-5.074-4.375-4.028(3)Commercial(4)Industrial

Specification Specification Specification Specification
12
3
4Specification Specification Specification Specification
12
3
4-2.1420.510-4.158-3.504-3.182-2.4630.561-4.665-3.984-3.648-2.4630.561-4.665-3.984-3.648-2.7270.602-5.074-4.375-4.028-3.641
0.037-4.158-3.504-3.182-3.626
0.104-4.665-3.984-3.648-3.7880.076-4.665-3.984-3.648-5.5390.003-5.074-4.375-4.028(Note) Shaded figures indicate that the null hypotheses are rejected with the associated criticalvalues.

As are the cases for the nationwide results, the null hypotheses are not rejected
at 10 percent level of significance in the all purposes and commercial lands. Particularly,
the p-values for the commercial lands are high, indicating that there are no cointegrating
relationships. On the other hand, the null hypotheses are rejected at 1 percent level inthe specification 2 and 4. The results for industrial lands show that the null hypotheses
are rejected at 5 percent level in the specification 1, at 10 percent in the specification 3,
and at 1 percent in the specification 4.
It is conceivable that the determinant factors other than those considered in
section 2 may have affected the commercial land prices in the local areas so that the
cointegrating relationships can be resumed once those factors are taken into account. We
now consider the possibilities that, even in the medium term, the regional commercial
lands can be affected by (a) bank lending, and (b) the fluctuations of land prices in thesix large city areas.29 We set up the following specifications for the commercial lands inthe local areas.

29

Kamada, Hirata, and Wago (2007) shows that Japanese land prices have high spatial correlation ina prefecture level by using spatial econometrics method.
29

p t = β 0 + β 1Trend t + NPV t + β 2 pop t + β 3c t + β 4 pu t + e t ,(17)where p t denotes the real land prices in the natural logarithm, Trendt denotes thetrend term, NPV t denotes the discounted present value of land in the natural logarithm,
pop t denotes the share of working-age population to the total population in the natural

logarithm, c t denotes the share of bank lending to the income within the prefecture,
pu t denotes the weighted-average real land price indicator of the six large city areas in

the natural logarithm, e t denotes the estimation residuals.
We conduct the cointegration tests with the above new regression setup for theregional commercial lands with/without the constraint on the discounted present valueof land and/or the inclusion of the demographic factor.
(Table 5) Results of Cointegration Tests (Local Areas, Commercial)
Specification Specification Specification Specification
1
2
3
4

ADF(t-value )p-value
Critical Value

1%
5%
10%

-4.2540.064-5.074-4.375-4.028-4.2740.122-5.460-4.740-4.384-3.7190.291-5.460-4.740-4.384-4.5830.127-5.826-5.086-4.721(Note) A shaded figure indicates that the null hypothesis is rejected with the associated critical value.

The results show that the null hypothesis is rejected at 10 percent level ofsignificance in the case with the restriction on the cointegrating vector of the discounted
present value and without the demographic factor (Table 5).
(5) Estimation of Cointegrating Vectors
We estimate the cointegrating vectors in this section. If two variables are identified as
cointegrated, the cointegrating vectors estimated by OLS are consistent. The estimatedresiduals and vectors, however, are not normally distributed and therefore a usualt-distribution is not used for any tests for the coefficients. In order to overcome thisshortcoming, Stock and Watson (1993) proposed the dynamic ordinary least squares
method (DOLS). The DOLS is the ordinary least squares method with leads and lags ofthe dependent variables. Leads and lags are decided based on the Schwarz information
criteria (SIC). The estimated cointegrating vectors by the DOLS are efficient and tested
with the normal distribution using the heteroskedasticity and autocorrelation consistentvariance-covariance errors. The results are reported as follows (Table 6 and 7). The
DOLS estimations are estimated for the specification 3 and 4 where the vectors on the30discounted present values are not restricted to one. Here we only estimate the vectors
for the six large city areas and the local areas, not nationwide, since the cointegrating
relationships are different from region to region.
(Six Large City Areas)
All the coefficients of the estimated regressions are significant at the conventionalsignificance levels. The sizes of the cointegrating vectors are different from the DOLS
and the OLS. The DOLS coefficients of the discounted present values for residential
and commercial land are larger than those of the OLS, while the DOLS coefficients ofthe share of the working-age population to the total population are smaller than those of
the OLS. The DOLS coefficients of the discounted present values for industrial lands
are somewhat smaller than those of the OLS.
(Local Areas)
The DOLS coefficients of the discounted present values for residential lands are smaller
than those of the OLS, while the DOLS coefficients of the share of the working-age
population to the total population are larger than those of the OLS. These results areopposite to those in the six large city areas. While the coefficients of the discounted
present values for commercial land are not significant in the specification 4, those are
significant in the specification 3. The DOLS coefficients of the discounted present
values for industrial land are not significant. The recent developments of industrial
lands in the local areas, particularly after 2000, showed the accelerated declines
contrasted with other uses and regions. Such developments may reflect the pessimistic
view on the manufacturing industry in the local areas with the backdrop of expanding
globalization and associated movement of the Japanese firms to expand the overseas
operations, particularly of labor intensive sectors.

31

(Table 6) Results of Cointegrating Vectors (Six Large City Areas)(1)Residential
Specification1

Specification2―――

Specification3

Specification4

OLS
Y
D
Constant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
Constant
Trend
Adj. R-squared
S.E.

-5.33
(0.08) ***-0.01(0.00) ***
0.32
0.25

1.36
(0.02) ***0.08-10.71(1.44) ***-0.01(0.00) ***
0.47
0.22

―
―
―
―
―
―

―
―
―
―
―
―

Specification1

Specification2

―
―

―
0.14
(0.03) ***-15.70(1.90) ***-0.03(0.00) ***
0.75
0.29

(0.18) ***―-8.43(1.57) ***-0.03(0.01) ***
0.83
0.23
1.50

(0.10) ***―-9.33(0.88) ***-0.04(0.00) ***
0.95
0.10

1.27
0.07
-12.44
-0.02
0.86
0.21

(0.12) ***(0.03) **(2.41) ***(0.01) ***

1.49
0.06
-13.35
-0.04
0.96
0.08

(0.08) ***(0.02) ***(1.62) ***(0.00) ***(2)Commercial
Specification3

Specification4

OLS
Y
D
Constant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
Constant
Trend
Adj. R-squared
S.E.

-5.52
(0.11) ***-0.03(0.00) ***
0.61
0.36

1.72

(0.24) ***―-11.71(2.03) ***-0.06(0.01) ***
0.64
0.32

―
―
―
―
―
―

―
―
―
―
―
―

―
-14.41(2.54) ***-0.08(0.01) ***
0.76
0.24

Specification1

Specification2

Specification3

―
―

―
0.11
(0.02) ***-12.69(1.45) ***-0.03(0.00) ***
0.78
0.22

2.06

(0.29) ***

1.56
0.13
-19.24
-0.05
0.77
0.26

(0.15) ***(0.04) ***(3.21) ***(0.01) ***

1.90
0.11
-20.81
-0.07
0.88
0.17

(0.14) ***(0.03) ***(1.95) ***(0.01) ***(3)Industrial
Specification4

OLS
Y
D
Constant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
Constant
Trend
Adj. R-squared
S.E.

-4.96
(0.09) ***-0.03(0.00) ***
0.65
0.28
―
―
―
―
―
―

―
―
―
―
―
―

0.99

(0.17) ***―-4.89(1.45) ***-0.03(0.01) ***
0.52
0.28
0.79

(0.10) ***―-2.75(0.90) ***-0.03(0.00) ***
0.77
0.12

0.84
0.11
-11.70
-0.02
0.71
0.22

(0.13) ***(0.02) ***(1.68) ***(0.01) ***

0.79
0.09
-9.44
-0.03
0.92
0.07

(0.07) ***(0.02) ***(1.23) ***(0.00) ***(Note 1) Y: Discounted present value of land in the natural logarithm, D: Share of working-age
population.
(Note 2) Leads and lags of the DOLS are chosen based on the SIC.
(Note 3) *, **, and *** respectively indicate that coefficients are significant at 10 percent, 5 percent, and1 percent level. The numbers in the above parentheses are standard errors.

32

(Table 7) Results of Cointegrating Vectors (Local Areas)(1)Residential
Specification1

Specification2

Specification3

Specification4―
0.04(0.01) ***-8.27(0.85) ***-0.02(0.00) ***
0.74
0.13

1.09

0.84
0.06
-8.41
-0.01
0.94
0.13

(0.16) ***(0.03) *(1.34) ***(0.01) *0.51
0.16-11.85
0.00
0.97
0.07

(0.16) ***(0.05) ***(2.07) ***(0.01)OLS
Y
DConstant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
Constant
Trend
Adj. R-squared
S.E.

―
―
-5.71
(0.04) ***-0.01(0.00) ***
0.69
0.14
―
―
―
―
―
―

―
―
―
―
―
―

Specification1

Specification2(0.12) ***―-6.50(1.02) ***-0.02(0.01) ***
0.93
0.14
1.00

(0.10) ***―-5.59(0.82) ***-0.02(0.01) ***
0.94
0.11

(2)Commercial
Specification3

Specification4

0.81

0.50
0.07
0.01
0.41
-7.09
-0.03

OLS
Y
D
C
Pu
Constant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
C
Pu
Constant
Trend
Adj. R-squared
S.E.

―
―
0.02
0.33
-7.03
-0.06

―
0.00 ***
0.03 ***(0.12) ***(0.00) ***

0.02
0.02
0.29
-8.34
-0.06

(0.02) ***(0.00)(0.04) ***(0.92) ***(0.00)

0.96
0.11

0.96
0.11

―
―
―
―
―
―
―
―

―
―
―
―
―
―
―
―

Specification1(0.11) ***
―

0.02
0.41
-5.54
-0.05

(0.00) ***(0.05) ***(0.86) ***(0.01) ***
0.93
0.11

0.95

0.95
0.10
(0.12) ***

―
0.03
0.36
-6.56
-0.06

(0.12) ***(0.02) ***(0.00) ***(0.05) ***(0.85) ***(0.01) ***(0.00) ***(0.07) ***(0.91) ***(0.01) ***

0.06
0.08
0.01
0.58
-4.00
-0.02

(0.15)(0.02) ***(0.00) ***(0.07) ***(1.41) **(0.01) ***

0.98
0.05

0.99
0.03

Specification2

Specification3

Specification4―
0.04(0.02) **-8.24(1.21) ***-0.04(0.00) ***
0.87
0.18

0.88

0.32
0.14
-8.73
-0.01
0.84
0.14

(0.11) ***(0.02) ***(0.90) ***(0.00) **

-0.11
0.24
-11.32
0.00
0.84
0.09

(0.13)(0.04) ***(1.57) ***(0.00)(3)Industrial
OLS
Y
D
Constant
Trend
Adj. R-squared
S.E.
DOLS
Y
D
Constant
Trend
Adj. R-squared
S.E.

―
―
-5.46
(0.06) ***-0.03(0.00) ***
0.86
0.19
―
―
―
―
―
―

―
―
―
―
―
―

(0.10) ***―-4.43(0.88) ***-0.03(0.00) ***
0.69
0.19
0.69

(0.09) ***―-2.62(0.83) ***-0.02(0.00) ***
0.63
0.15

(Note1) C: Ratio of credit to the nominal GDP, Pu: Land price of commercial area in the six large city
areas.
(Note 2) Leads and lags of the DOLS are chosen based on the SIC.
(Note 3) *, **, and *** respectively indicate that coefficients are significant at 10 percent, 5 percent, and1 percent level. The numbers in the above parentheses are standard errors.

33

The theoretical values of the real land prices using the estimated cointegrating
vectors are shown in Figure 15. Many of the estimated values are above the actual realland prices.30 The levels of the estimated theoretical values of the real land prices,
however, are different by a large margin with different specifications of the estimation
models. In addition, it is well known that the end point estimations by the cointegration
analysis can be changed very much once the new data are added. Therefore, dueconsiderations are needed to evaluate the difference between the theoretical values ofreal land prices and the actual prices.

30

The cointegrating vectors, which are used for the calculations of the theoretical values of the realland prices, are estimated by the OLS for specification 1 and 2, and by the DOLS for specification 3
and 4. We use the vectors estimated by the OLS for regional commercial and industrial lands withspecification 4 since the DOLS coefficients of the discounted present values are not significant.
34

(Figure 15) Theoretical and Actual Values of Real Land Prices

Six Large City Areas

Local Areas(1) Residential
5.5(1) Residential（Natural Logarithm）

5.0

5.0

4.5
①
④ 4.0
③
② 3.5

4.5
4.0
3.5

①③
②
④

3.0

3.0

2.5

2.5

2.0

2.0
60

65

70

75

80

85

90

95

00

60

05

year

(2) Commercial
5.0（Natural Logarithm）

65

70

75

80

85

90

95

00

(2) Commercial（Natural Logarithm）

4.5

4.5

（Natural Logarithm）

4.0

4.0

3.5
①
③
④ 3.0
②
2.5

3.5
3.0
2.5
2.0

①②
④
③

2.0

1.5
60

65

70

75

80

85

90

95

00

60

05

65

70

75

80

85

90

95

00

(3) Industrial

05

year

year

5.0

05

year

(3) Industrial（Natural Logarithm）

4.5

4.5

③
①
④
②

4.0
3.5

（Natural Logarithm）

4.0
③
①
②
④

3.5
3.0

3.0

2.5

2.5
2.0

2.0
60

65

70

75

80

85

90

95

00

05

60

65

70

75

80

85

90

95

00

05
year

year

(Note) The numbers in the figures correspond to the specification 1, 2, 3, and 4, respectively. The
bold lines are actual real land prices.

(6) Estimation of Error-Correction Models
We estimate the error-correction models to explain the short-term land price fluctuations
using the estimated cointegrating vectors. The dependent variables are the year-on-year
growth rates of the real land prices. The independent variables are the error-correction
term (one quarter lagged), the year-on-year growth rate of the discounted present valuesof land, the change in the share of the working-age population to the total population,
the year-on-year growth rate of real bank lending, and the constant term.

35

Δp t = β 0 + β 1EC t −1 + β 2 ΔNPV t + β 3Δpop t + β 4 Δc t + ε t ,(18)

where Δp t denotes the growth rate of the real land prices (y-o-y), EC t −1 denotes theerror-correction term (lagged), ΔNPV t denotes the growth rate of the discounted
present value of land (y-o-y), Δpop t denotes the change in the share of theworking-age population to the total population, Δc t denotes the difference between thegrowth rate of the real bank lending and the growth rate of the discounted present valuesof land, and ε t denotes the estimation residuals.
The reason to use the change in real bank lending for an explanatory variable isthat there is a high correlation between bank lending and land price fluctuations in the
short term. Such a relationship, however, is not supposed to affect the medium tolong-term land price developments and therefore the factor is not included in the
cointegration analysis except for the commercial lands in the local areas. We conduct
the estimation using the difference between the growth rate of bank lending and thegrowth rate of the discounted present values of land as a bank lending factor in theerror-correction models.31 The reason is that the changes in the economic fundamentals
are reflected in the changes in the discounted present values of land, and the further
fluctuations in bank lending over the changes in the discounted present values of land
are supposed to be a factor affecting the land price fluctuations independently besides
the economic fundamentals.
The estimations of the error-correction models are conducted by region andusage. The error-correction terms ( EC t −1 ) are chosen based on the results of thecointegration analysis; the cointegrating vectors with the lowest p-values are chosen. As
a result, the followings are chosen32;(Six Large City Areas)
Residential: specification 3, Commercial: specification 4, Industrial: specification 1(Local Areas)
Residential: specification 2, Commercial: specification 1, Industrial: specification 1
31

For the estimations of the regional land price changes, we aggregate the bank lending byprefectures into the six large city areas or the local areas using “Deposits, Loans and Discount
Outstanding of Domestically Licensed Banks by Prefecture (the Bank of Japan)”.
32
While the specification 4 should be chosen for the regional industrial lands based on the result of
the cointegration analysis p-value, the estimated cointegrating vector is not consistent with the theory.
Therefore, we chose the cointegrating vectors with the lowest p-values among the specification 1, 2
and 3.
36

The estimation results are shown in table 8. The error-correction terms are
significant in all equations. The coefficients of the changes in the discounted present
values of land are correct (positive) in signs and significant. The demographic factors
are, however, not significant for residential lands in both the six large city areas and the
local areas. Based on the results so far, while the demographic factor has impact on thelong-term land price developments, it has little influence on the short-term land pricefluctuations for residential lands. This is an opposite result to Otake and Shintani(1996).
(Table 8) Estimation Results of Error-Correction Models(1) Six Large City Areas
Residential

Commercial

Industrial

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

ΔY

0.80

(0.21) ***0.94(0.27) ***0.83(0.23) ***

ΔD

0.02

(0.03)

0.13(0.04) ***0.06(0.03)

0.68(0.20) ***

-0.01
0.63
0.08

(0.02)**

0.44(0.25)

-0.05
0.63
0.09

(0.02) ***

ΔC

0.49

(0.19)C
Adj. R-squared
S.E.

-0.04
0.69
0.07

(0.01) ****(2) Local Areas
Residential

Commercial

Industrial

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

ΔY

0.87

(0.21) ***0.60(0.13) ***0.77(0.19) ***

ΔD

0.03

(0.03)

0.05(0.02) **0.07(0.03) **

ΔC

0.60

(0.18) ***0.54(0.11) ***0.69(0.18) ***0.36(0.06) ***

-0.03
0.87
0.04

***

―

ΔP u
C
Adj. R-squared
S.E.

-0.02
0.49
0.07

(0.01)(0.01)

―
-0.03
0.53
0.07

(0.01) **(Note 1) *, **, and *** respectively indicate that coefficients are significant at 10 percent, 5 percent,and 1 percent level. The numbers in the above parentheses are standard errors.
(Note 2) EC: Error correction term, ΔY: change in the discounted present value of land, ΔD: change
in the share of working-age population, ΔC: change in the ratio of credit to the nominal GDP,
ΔPu: change in the weighted-average land price indicator of the six large city areas(commercial).

37

To check the impacts of each factor on the land price fluctuations visually, thefactor contributions are calculated using the estimated coefficients of theerror-correction models (Figure 16). The results are as follows;(a) The surges in land prices from the mid 1980s to the late 1980s are attributable to theincrease in the discounted present values of land in that the expected growth rate ofincome increased while the nominal long-term interest rates were kept in low levels.
In addition, the unexplained factor (= residuals) has contributed to the surges. Forcommercial lands in the local areas, the increase in the six large city commercial
land prices is a significant factor during the period.
(b) In the late “bubble” period in the early 1990s, the increase in bank lending
contributed to the increase in land prices.33 On the other hand, the changes in the
discounted present values of land and the error-correction term show the downward
pressure on the land prices. Furthermore, the unexplained factor (= residuals) are
shown in the downward pressure on land prices.
(c) The recent developments show that the increase in the discounted present value ofland has contributed to the increase in land prices since the real economy has grownsteadily with very accommodative financial conditions. In addition, theerror-correction term has contributed to the increase in land prices in the recent past.
While the bank lending factor has been a downward contributor for the land prices
since the mid 1990s, such a movement has finally halted in 2005. The demographic
factor has contributed to the declines in the land prices since the mid 1990s.

33This tendency is conspicuous in the local areas.
38

(Figure 16) Contributions of Y-O-Y Land Price Changes
Six Large City Areas

Local Areas(1) Resdential
50(1) Resdential（y/y,％）

30
Bank Lending
Demographic
Discounted Present Value

40
30

Bank Lending
Demographic
Discounted Present Value

25
20

ＥＣ term
Estimated
Actual20（y/y,％）ＥＣ term

15

Estimated
Actual

10

10

5
0

0

-10

-5

-20

-10

-30

-15
-20

-40
1980

1985

1990

1995

2000

1980

2005

1985

1990

1995

2000

year

(2) Commercial
50

2005
year

(2) Commercial（y/y,％）

30
Bank Lending
Demographic
Discounted Present Value

40
30

Land price of six large city areas
Bank Lending
Demographic
Discounted Present Value
ＥＣ term
Estimated
Actual25
20

ＥＣ term

15

Estimated
Actual20（y/y,％）

10

10

5
0

0

-10

-5

-20

-10

-30

-15
-20

-40
1980

1985

1990

1995

2000

1980

2005

1985

1990

1995

2000

year

(3) Industrial
50

2005
year

(3) Industrial（y/y,％）

30
Bank Lending
Demographic
Discounted Present Value

40
30

25

Bank Lending
Demographic
Discounted Present Value

20

ＥＣ term
Estimated
Actual20（y/y,％）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

39

6．Conclusion
This paper conducts the time series analysis on the weighted-average land priceindicators, which are supposed to be appropriate indicators in the context of the macro
economic analysis. The cointegration analysis shows that there are cointegrating
relationships between real land prices and the discounted present values of land, whichmove in line with economic fundamentals. In addition, the demographic factors havesignificant impacts on the land prices even in the long term. We have also shown thatthe error-correction models using the cointegration relationships explain the actual land
price fluctuations very well. The short-run fluctuations of land prices are attributable tothe changes in economic fundamentals such as income and interest rates, and thechanges in bank lending and demographics in addition to the error-correction
movements.
We will clarify the relationship between our analysis here and the “bubble.” We
exclude the explosive bubble solutions as is obvious in equation (4) and (5). This point
is consistent with the results that there are cointegrating relationships between the actual
land prices and the theoretical land prices. However, it is true that the actual land prices
can deviate from the theoretical land prices. In fact, the error terms in the cointegration
analysis show large cyclical fluctuations. We, therefore, need to take into account thatthe actual land prices can deviate from the theoretical values even during several years.
Next, we need to pay attention to the fact that the theoretical value of land calculated
here is based on rather myopic expectations of the future income. This is obvious fromthe fact that we use the nominal long-term interest rates and the expected nominal GDP
growth for each period. This specification has pros and cons. The pros are that thisspecification can describe the anecdotal evidence very well during the “bubble” period,
the land prices grew with the expectation that high nominal growth would continue
coincided with the low levels of the nominal long-term interest rates. It is highly
probable that the actual economic activities were conducted with such expectations atthat time. The cons, on the other hand, are that the theoretical values of land with such amyopic expectation can be different from those in the long-run expectations of theeconomy. In the long run, the denominator of equation (7) should be constant if thecyclical movements are averaged out unless tax rates and long-term risk premiumchange permanently. The actual data, however, show that the denominator of equation(7), that is the ratio of real land price to the real GDP, is not constant over time. We will
leave a research on the long-run trend change in the land price to the GDP ratio as a
future topic.

40

Appendix 1: Weighted-Average Land Price Indexes and Other Land Price Indicators
As described in the main text, the weighted-average land price indexes are appropriate
land price indicators when one analyzes land price developments in terms of macro
economic perspective. In this appendix, we explain the differences between theweighted-average land price indicators and other land indicators in detail.
(Discussion of Land Price Indicators as Appropriate Macro Economic Indicators)
The weighted-average land price indicators evaluate the change in land prices of the
low-priced lands with smaller weights and the changes in land prices of the high-priced
lands with larger weights. On the other hand, the official land price indicators such as
the Urban Land Price Index by the Japan Real Estate Institute and the Published Land
Prices by the Ministry of Land, Infrastructure and Transportation put the same weights
on both high-priced lands and low-priced lands. Therefore, the changes in the prices ofhigh-priced lands are underestimated, while those of low-priced lands areoverestimated.
Representative macro land indicators are the land values of the system of thenational account (SNA) and they are good benchmarks to compare other land priceindicators. First, we compare the regional weights of the SNA land values and those of
the Published Land Prices officially published.34 The weights of the Published Land
Prices are almost equivalent to the weights of the populations of the regions (Appendix
1 Figure 1) as the white dots are concentrated along with 45 degree line. If we calculate
the weights of the same regions using the SNA land values, we have a different picture.
The weights of the low-priced regions’ lands are overvalued as the black dots arelocated above the 45 degree line, while the weights of the high-priced regions’ lands areundervalued as the black dots are far below the 45 degree line. Second, we compare theregional weights of the SNA land values and those of the weighted-average land priceindicators (Appendix 1 Figure 2). The weights of the SNA land values correspond to
those of the weighted-average land price indicators as the black dots are located almost
exactly along with the 45 degree line. This shows that the appropriate land priceindicators are the weighted-average land price indicators when one analyzes the impactsof land prices on the macro economy.
Some specialists of land evaluation claim that it is unnecessary to recalculate
the weights of lands using land prices since the choices of survey spots are evaluated by
34

The weights are calculated as the shares of numbers of survey points of the regions to the total
numbers of survey points in the nationwide.
41

specialists and the numbers of the survey spots actually represent their importance.
Appendix 1 Figure 2

（％）

40

Weight share of weighted-average land prices

Weight share of officailly published l;and prices

Appendix 1 Figure 1

Pop ulation share

35

SNA share

30
25
20
15
10
5
0

（％）

40
35
30
25
20
15
10

Pop ulation share
SNA share

5
0

0

5

10
15
20
25
30
Pop ulation share, SNA share

35

40

0

（％）

5

10
15
20
25
30
Pop ulation share, SNA share

35

40

（％）

(Note) The weights are calculated for 13 regions (average from 1980 to 1992): Hokkaido, Tohoku,
Ibaraki-Tochigi-Gunma, Saitama-Chiba-Kanagawa, Tokyo, Yamanashi and Nagano, Chubu,
Hokuriku, Kinki, Chugoku, Shikoku, Kyushu, and Okinawa.

As shown in the previous figures, however, the weights of the official land priceindicators are in line with the population weights and they are not necessarily
appropriate land price indicators when analyzing their impacts on the macro economy.
(Issues on the SNA Land Values)
It has been considered that the SNA land values were appropriate macro economic
indicators to see the developments of land prices and they moved along with theweighted-average land price indicators until the burst of the bubble in the early 1990s.
The developments of the SNA land values after the burst of the bubble, however, did not
decline so much while the weighted-average land price indicators plunged. In someregions, the SNA land values increased, while the weighted-average land priceindicators and even official land price indicators declined (Appendix 1 Figure 3). In themid 1990s, there were many incidents that uses of lands were changed from agriculturaluses to commercial uses in the local areas where constructions of shopping malls werevery active. While such a transformation of lands could lead to the increase in the land
values in the local areas, the magnitudes of the changes are too large. This could suggestthat the estimation of the SNA land values may have problems.3536
35

Until 1995, the SNA estimation for commercial lands used the land evaluation values used for42Appendix 1 Figure 3
Hokkaido,Tohoku
250

Kanto

(1980=100）(1980=100）

350
300

200

250
150

200

100

150
100

50

50
0

0
1980

1985

1990

1995

1980

2000
2005
year

250

1990

1995

2000

SNA
W eighted-average land prices
Officially publis hed land prices

SNA
W eighted-average land prices
Officially published land prices

Chubu,Hokuriku

1985

2005
year

Kinki

(1980=100）

400(1980=100）

350
200

300
250

150

200
100

150
100

50

50
0

0
1980

1985

1990

1995

2000

2005

1980

1985

year
SNA
W eighted-average land prices
Officially published land prices

300

250

250

200

200

150

150

100

100

50

50

0
1985

2000

2005
year

Kyushu,Okinawa(1980=100）

1980

1995

SNA
W eighted-average land prices
Officially publis hed land prices

Chugoku,Shikoku
300

1990

1990

1995

2000

2005

year
SNA
W eighted-average land prices
Officially published land prices(1980=100）

0
1980

1985

1990

1995

2000

SNA
W eighted-average land prices
Officially publis hed land prices

2005
year

taxation, which were supposed to be overestimated compared to the market prices of land. This
could be a reason to overestimate land values in the SNA until the mid 1990s.
36
Nishimura and Shimizu (2002) pointed out that the sequence of residential land price data of the
Published Land Prices might have a break in the early 1980s since the survey spots were changed
during the time.
43

Appendix 2: Estimation of Interest Rate Gap before Financial Liberalization
In this appendix, we explain how to estimate the interest rate gap before the financial
liberalization in the early 1980s. We use it to calculate the discounted present values ofland.
Many studies37 claim that the credit rationings were prevailing before thefinancial market liberalization and the interest rates were regulated at lower levels thanas were supposed to be under the liberalized financial market. In fact, the levels of thelong-term nominal interest rates are far below the expected growth rate of the nominal
income before the 1980s (Appendix 2 Figure 1).
Appendix 2 Figure 1
22
20
18
16
14
12
10
8
6
4
2
0
-2

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

1957

1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

2001

2005
year

Kanemoto (1990) presents three hypotheses that the levels of the interest rates
are far lower than the growth rates of land prices as follows; (a) the increases in land
prices are not expected in advance, (b) the uncertainty of land price fluctuations islarge and the risk premium of lands is high, and (c) since the capital and financial
markets are imperfect and heavily regulated, the effective interest rates are muchhigher than the observed interest rates. He claims that, since the differentials between
the growth rates of land prices and interest rates were maintained for a very long time,(c) would be an appropriate reason for such differentials.
Based on the argument above, we estimate the interest rate gap before theliberalization of the financial market as follows.
Step1: The following equation is estimated, assuming that the relationship between thenominal interest rate gap and the output gap is expressed as a liner relationship.
37

See Tachi and Komiya (1971), Tachi and Hamada (1972), and Ito and Ueda (1982).
44

LG t = β 0 + β 1GAP t ,(19)

where LG t denotes the nominal long-term interest rate gap (= q t − f te = i t − g te ), and38
GAP t denotes the output gap.

Step2: Using the estimated parameters ( βˆ 0 , βˆ 1 ) and the output gap before theliberalization of the Japanese financial market, the estimated long-term interest gap(est ( LG t )) is calculated as follows (Appendix2 Table1)est ( LG t ) = βˆ 0 + βˆ 1GAP t(20)

Appendix 2 Table 1: Results of the Interest Rate Gap Estimation
CoefficientStandard Error

GAP-0.555(0.109)Constant

1.721(0.113)

Adj. R^2

0.213

S.E.

1.089

Using the nominal interest rate gap,39 we calculate the discounted present value of land(Appendix 2 Figure 2).
Appendix 2 Figure 2: Estimated Interest Rate Gap
6
4
2
0
-2
-4
-6
-8
-10
-12

(%)

Nominal Long-term Interest Rate Gap
Estimated Nominal Lomg-term Interest Rate Gap
Output Gap

1957

1961

1965

1969

1973

1977

38

1981

1985

1989

1993

1997

2001 2005year

The output gap is the difference in percent between the actual GDP and the potential GDP
calculated by HP filter (λ＝1,600).
39
In this estimation, we do not specify whether the output gap causes the interest rate gap or theother way around, and we simply use the correlation between them. It would be appropriate that bothroutes are working.
45

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49