172
2021 年 7 月

Demographics, Property Prices, and Credit Conditions-Analysis Based on Panel Data from 17 Countries Over a Half-Century-

Yongheng Deng
(Wisconsin School of Business, University of Wisconsin-Madison)
Tomoo Inoue(Faculty of Economics, Seikei University)
Kiyohiko Nishimura(National Graduate Institute for Policy Studies: GRIPS)
Chihiro Shimizu(Center for Spatial Information Science, The University of Tokyo)
0Demographics, Property Prices, and Credit
Conditions: Analysis Based on Panel Data
from 17 Countries Over a Half-Century∗
Yongheng Deng†, Tomoo Inoue‡, Kiyohiko Nishimura§, Chihiro Shimizu¶
July 1, 2021
Abstract
Using panel data from 17 countries with varying economic circumstances from 1974 to
2019, we estimate regression models that explain residential property price dynamics byincorporating demographic factors and considering the interaction of those demographics
with credit conditions. Our results show the importance of the demographic factors inmodeling the long-run equilibrium of residential property prices. We ﬁnd that the eﬀect
of nominal interest rates determined by monetary policy on asset prices varies dependingon the country and the degree of population aging at the time. We also ﬁnd that thepersistently optimistic population projections lead to the oversupply of the residential
stock in rapidly aging countries, resulting in stagnant residential property markets.
Journal of Economic Literature Classiﬁcation Numbers: E31, R21, R31
Keywords: population aging, residential property prices, nominal interest rates, credit
cycle, panel cointegration analysis∗ We are grateful to Nobuhiro Kiyotaki for important suggestions on the starting point of this paper. We

would also like to thank Erwin Diewert, James D. Hamilton, Robert Hill, Naohito Abe, Iichiro Uesugi,
Tomohiro Hirano, Tatsuyoshi Okimoto, Jiro Yoshida, Masaki Mori, and Daisuke Miyagawa for theirhelpful comments. This paper is based in part on the research results of Grant-in-Aid for ScientiﬁcResearch (A): 20H00082, Japan Society for the Promotion of Science.
† Wisconsin School of Business, University of Wisconsin-Madison.
‡ Faculty of Economics, Seikei University§ National Graduate Institute for Policy Studies (GRIPS)¶ Center for Spatial Information Science, The University of Tokyo, and Nihon University.

11 Population Dynamics, Property Prices, and the Eﬀects ofNominal Interest Rates
The world economy is facing the unprecedented challenge of changing population dynamics, with some countries experiencing a rapid rise of the young population while others arefacing rapid aging. In such uncharted territory, it is crucial to ask: Is the eﬀect of the change
in nominal interest rates (determined by monetary policy) similar across countries or vastly
diﬀerent? Why is the recovery from collapse of the so-called property bubbles inconsistentacross countries? Casual observation shows that property prices are not recovering to the prebubble era in rapidly aging economies as fast as in other economies, and their adjustment has
taken very long (Crowe et al., 2013[6]). However, existing research has not provided suﬃcientanswers to such questions. We attempt to answer these questions from an econometric approach through the experience of 17 divergent economies over 46 years, focusing on population
dynamics statistics.
During the post-World War II rapid economic growth era, Japan experienced the largest
property bubble of the 20th century (Shimizu and Watanabe, 2010[34]). However, following thecollapse of the bubble in 1990, the Japanese economy faced an extended period of economic
stagnation termed the “lost decade.” At the peak of the Japanese bubble, land in central
Tokyo was sold for as much as 50 million yen (about US $500,000) per square meter; however,property prices plummeted after the bubble’s collapse, especially in regional markets. In the
21st century, Japan’s population was in a period of both fast aging (the fastest rate in theworld) and absolute decline. In light of this, the number of vacant houses has continued toincrease to depress regional property markets, and it has been predicted that in 10 years,
one-quarter of all residential houses will be vacant. Furthermore, ownership of more than
10% of the nation’s land has been relinquished by the owners The population decline inJapan’s regional cities and the aging trend had already begun in the second half of the 20th
century. Some municipalities became ﬁnancially insolvent in the early 21st century, leading
to the coining of the phrase “extinct municipalities.” In 2010, the town of Yubari in thenorthern Japanese region of Hokkaido suﬀered ﬁnancial insolvency. Looking at the population
composition reveals that this insolvency occurred when the old age dependency ratio, whichindicates the proportion of the old population (ages 65 and over) to the working-age population(ages 15 to 65), was at a level exceeding 90%. In the context of these phenomena, we explore
what kind of economic mechanisms—including demographics—are at work, focusing on theirproperty markets.*1
From the global perspective, Japan and Sweden in the late 20th century and various Westerncountries, including the United States, in the early 21st century (after the global ﬁnancial crisisof 2007) faced the formation of property bubbles and then long-term economic stagnation
following the collapse of those bubbles. According to Claessens et al. (2011)[4], not all
property bubbles lead to ﬁnancial crises, and not all ﬁnancial crises are caused by property
bubbles. However, in many countries, economic slumps together with property market failures
triggered by the formation and collapse of property bubbles are signiﬁcant in terms of length*1 In recent years, there are many “superstar” cities such as New York, Boston, Washington, D.C., San

Francisco, and Seattle in the United States, London, Frankfurt, and Amsterdam in Europe, and Tokyo,
Seoul, Beijing, Singapore, Sydney, and Melbourne in Asia Paciﬁc, where residential prices have dramatically increased. However, there is substantial regional heterogeneity, making price behavior very
diﬀerent between these superstar cities and the national average. This study is about the national
average of residential property prices, not that of these superstar cities.

2and scope (Crowe et al., 2011[5]).
Even before the global ﬁnancial crisis triggered by the collapse of Lehman Brothers, numerous studies have attempted to properly understand the correlation between long-term overall
economic stagnation and the mechanisms underlying large ﬂuctuations in asset prices, suchas property bubbles. Reinhart and Rogoﬀ (2009)[31] attempt to understand the relationshipbetween the two based on long-term economic data from multiple countries, covering over
100 years. Reinhart and Rogoﬀ (2009)[31] elucidate four common phenomena observed incountries that suﬀered ﬁnancial crises: 1) among asset prices, property prices in particulardiverged signiﬁcantly from earnings; 2) debts increased far beyond income/net assets, andleveraging increased; 3) substantial capital inﬂows continued, and 4) productivity increases
lagged behind increases in asset values and debts. Furthermore, the study clariﬁes that whensociety as a whole is excessively optimistic, it leads to high growth via ﬁnancial leverage, which
fosters growth in a self-feeding manner. Conversely, the authors also note that once optimism
turns into pessimism, regardless of the reason, the economy enters a cycle of contraction.
There are several theoretical frameworks to explain Reinhart and Rogoﬀ’s (2009)[31] ﬁndings. For example, Kiyotaki and Moore (1997)[18] provide a micro foundation theory ofleveraging and de-leveraging during credit cycles. When leverage is high for the economy,
even a small adverse shock makes economic conditions deteriorate sharply to induce accelerated de-leveraging. During the de-leveraging process, many assets, including property, aresometimes on “ﬁre-sale,” causing lasting damage to property markets.
Nishimura (2016)[24], drawing on the author’s experience managing monetary policy,*2 analyzes the systems, policies, and histories of the United States, various European countries,
and Japan, noting the presence of two common factors in countries facing economic crises: (1)excessive optimism caused by favorable changes in population composition (rapid increase inyoung population) and (2) rapid expansion of credit due to the spread of so-called new ﬁnancetechnologies and vehicles*3 introduced during the excessively optimistic time. The author
also alludes to the relationship between these factors and rapid increases in property prices.
Particularly, the rapid expansion of credit corresponds to the ﬁnancial instability theory of
Minsky (1992)[22]. The author then indicates that the ﬁnancial crises from the late 20th
century through the early 21st century were likely to happen given the presence of the strong
cumulative interaction of factors such as dramatic shifts in population composition, property
bubbles, and credit cycles.
In comparison, let us consider the Japanese experience. The post-war era of rapid economic growth was driven by the generation born during the postwar baby boom reaching theworking age. This period is known as a “population bonus phase” (Ito and Hoshi, 2020[16]).
Then, in the early 1980s, this baby-boomer generation became home buyers and entered the
housing market, generating the highest level of housing demand since the war and triggering
the formation of a property bubble. At that time in Japan, optimism was extremely high.
Following the collapse of the bubble in 1990, Japan’s working-age population has continued
to decline. In recent years, in conjunction with deﬂation and a low economic growth rate,
the property market has struggled with a high vacant house rate and increase of land withrelinquished ownership: It has entered the “population onus phase.” With the appearanceof these problems, a pessimistic mood has spread across society. Considering these facts, it*2 Kiyohiko Nishimura was a member of the Bank of Japan’s Policy Board from 2005 to 2008; additionally,

from March 2008 to March 2013, he was a Deputy Governor of the Bank of Japan. Including his timeon the Policy Board, he was involved in monetary policy for eight years.
*3 For example, large time deposits with no interest rate ceiling were introduced and Commercial Papers
were allowed for large corporations around 1986, at the beginning of the so-called bubble economy inJapan.

3

follows logically that there is a close relationship between population factors, large property
market ﬂuctuations, and economic downturns.
The literature review suggests that demographics and the property market have a strong
underlying inﬂuence on macroeconomic ﬂuctuations such as economic growth and length ofrecessions. We attempt to decipher this mechanism by focusing on the relationship between theresidential property market and demographics. We investigate the following two hypotheses,
using panel data from 17 countries spread over 46 years.
(1) Did changes in population composition inﬂuence the dynamics of residential property
prices?
(2) Did changes in population composition amplify/dampen nominal interest rates’ eﬀects
on residential property prices?
This study’s key contributions are highlighted below. First, there is no consensus among theories that simultaneously explain demographic changes, property price dynamics, and credit
cycles; and this theoretical strand is still being developed and is not ready for testing using
data. Therefore, we base our study on the most basic theoretical relationships involved in
the present value relationship (PVR) model (Walras, 1954[38]; Campbell and Shiller, 1988[2]).
Using international panel data from 17 countries with diverse population compositions, population trends, economic growth rates, and housing market environments, over almost halfa century, this study empirically examines the relationship between demographics, property
price dynamics, and credit cycles. In the previous research, only limited residential property
price data are obtained for a limited period. It is therefore only possible to analyze at mostone property boom and bust cycle. However, this study’s dataset includes various cases, including countries with an increasing young population, countries that have already reacheda high aging rate, and countries that have experienced two or more property boom and bustcycles in the period under study. Thus, it enables us to consider various cases necessary forthis kind of analysis of slow-moving long-term factors.*4
Second, to the best of our knowledge, this study is the ﬁrst to analyze the eﬀects of expectation errors in demographics. Mankiw and Weil’s (1989)[21] central criticism of demographics
and housing market-related analysis focuses on the fact that if economic agents’ expectations
are rational (that is, with no persistent expectation errors) with respect to demographic projections, there should be little impact of demographic changes on residential property prices,since the supply will be adjusted accordingly when supply is suﬃciently elastic. However, we
ﬁnd some evidence that demographic expectations are not rational and, for example, expectation errors about populations persist. (See Figure 1) Thus, when young populations are
growing and underestimation of demad persists, housing supply shortage accumulates overtime to cause an increase in residential property prices. In contrast, when population is aging
rapidly and overestimation of demand persists, housing supply surplus becomes persistent todepress residential property prices. Therefore, to assess the eﬀects of possible persistent demographic expectation errors, we collect data by tracing population projection data publishedby each country throughout the analysis period, as far back as possible, and estimate thediﬀerence between the actual ﬁgure and the ones projected before.
Third, after assessing the long-term relationship between residential property prices anddemographic factors, this study examines the interactive eﬀect of demographic factors and*4 After the ﬁnancial crisis, the International Monetary Fund (IMF) and Bank of International Settlements(BIS) took the lead in developing the property price index internationally. BIS and the Organisation for
Economic Co-operation and Development (OECD) began publishing the property price index in 2016(see Diewert et al., 2020[8]).

4nominal interest rates. Particularly, we examine whether the impact of declining nominalinterest rates on residential prices are substantially smaller in an aged economy, like presentday Japan, than in an economy with a growing young population, like Japan thirty yearsago.

2 The Empirical Model
Mankiw and Weil (1989)[21] examine the relationship between demographics and the property market in their seminal work. They argue that in the 1980s, housing demand peaked dueto the baby-boomer generation in the United States; subsequently, over the next 20 years,
till 2007, real residential property prices decreased by 47% due to population decline. Thisso-called “asset meltdown hypothesis” subsequently caused a considerable debate (Mankiw
and Weil, 1989[21]).
Two major issues were central to this debate: supply elasticity and accuracy of projected demographic changes. Researchers argued that demographic changes take place at an extremely
slow pace, and, thus, they are accurately predictable. Therefore, if the housing supply iselastic, even in the event of a pessimistic future population projection, no residential property
price slump should occur, since supply will be adjusted via stock adjustment (Hendershott,
1991[13]; Hamilton, 1991[12]). Engelhardt and Poterba (1991)[9]’s empirical research reports
no statistically signiﬁcant relationship between demographic changes and residential property
price changes in Canada.
Studies focusing on Japan, such as Ohtake and Shintani (1996)[26], obtain similar results.
They conclude that, while demographic changes impact residential property price changes inthe short term—when supply constraints exist—they do not impact residential property prices
in the long run, since the housing supply is adjusted accordingly. Furthermore, Shimizu andWatanabe (2010)[34] estimate housing demand using Mankiw and Weil (1989)[21]’s frameworkand expand the model based on panel data (by prefecture in Japan and by state in the UnitedStates) and show that housing demand ﬂuctuation shocks do not impact residential property
prices in the long run.
However, Japan’s experiences in the most recent decade have cast doubts about the elasticity of the supply of houses in an increasingly rapidly aging society. Vacant houses and landwith unknown ownership are increasing at an unprecedented rate in Japan, raising doubts
about how elastic the housing supply is in a low-growth economy. Particularly, land, which
is one of the essential factors determining housing stocks, is a real, non-depreciable asset.
The supply volume is rather limited (physically or by zoning), so that it is inelastic rather
than elastic.*5 If this is the case, even when we assume that demographic changes are perfectly predictable, demographics may inﬂuence residential asset prices. In this context, Takáts(2012)[35] and Nishimura and Takáts (2012)[25], using a two-generation overlapping generation model, demonstrate that increases in the working-age population lead to rises in realresidential property price in the ultra-long run (between generations). However, it cannot
explain residential property price changes in the medium term (around 10 years) or over thebusiness cycle period (around two years), which is our study’s subject.*6*5 Gyourko, Mayer and Sinai (2013)[11] focus their attention that most pronounced residential price move-

ment is driven by the limited supply of land. Similarly, Knoll, Schularick and Steger (2017)[19] showsthat residential price movement over a century is mostly brought on by the movement of the land price,and the sharp increase in the last half of the 20th century in particular is caused by the substantial
appreciation of the land.
*6 Their model examines an intergenerational portfolio selection problem. Thus, while it can explain that
population composition changes have an impact on intergenerational or ultra-long-run price changes,

5Figure 1 Persistently Optimistic Predictions of the Total Fertility Rate by Government
Experts at the Unfavorable Time of Declining Rates (Japan)
Source: National Institute of Population and Social Security Research. Various issues.

Next, we consider the accuracy of projections of demographic changes. Figure 1 shows
population statistics experts’ predictions of the total fertility rate (TFR) starting in 1975,
when the fertility rate dropped noticeably, to 2012, when the drop was reversed. This ﬁgure
has several notable features of persistent projection errors at the unfavorable time of declining
TFRs: 1) the recent unforeseen changes are considered temporary, 2) the level will eventually
revert to a presupposed long-term level that is close to the “old normal” of the previous period,and 3), most importantly, even if the current period ﬁgure is constantly lower than the longterm level considered in the previous projection, the downward revision of the projection isvery slow.
The last point is crucial since government experts’ demographic projections, which are
indispensable for private-sector actors to anticipate long-term total demand and total supply
in an economy, may not be “rational” in the sense that expectation (projection) errors are notzero on average over a given period. The ﬁgure shows that overly optimistic projections persist
over the period of analysis, and optimistic errors accumulate when the situation is unfavorable
in terms of population dynamics. For instance, a projected TFR for the year 2010, made in
1992, was approximately 1.8. However, the actual TFR in the year 2010 was 1.4. Thisgap (0.4) is likely to lead to over-capacity and over-supply. This suggests another importantroute via which demographic factors inﬂuence the economy: When demographic dynamics areunfavorable, it is likely to be translated into over-capacity and over-supply through persistentand accumulated expectations errors. Thus, if government experts’ and regular people’s overly
optimistic forecast errors persist and are accumulated, residential property prices decline morethan in the contrasting scenario.
This study empirically investigates the demographic dynamics’ eﬀects on property prices
but unable to explain changes in the medium run and over business cycles.

6

considering the above-mentioned two points. Speciﬁcally, we elucidate that long-term nominal
residential property prices are determined by the perfect foresight PVR.*7 We start with thefollowing long-run equilibrium relation between the nominal residential property price index(P rppi ), consumer price index (CPI) (P cpi ), real rent (R)，nominal interest rate (i), andnominal expected rate of change in housing rents (g e ):*8 *9P rppi =P cpi × R.
i − ge(1)

As Equation (1) is for the no-arbitrage condition in the competitive equilibrium, it may beconsidered common to all capital markets. Accordingly, we assume that this basic relationshipis common to all the countries analyzed below; however, it will be tested statistically in thefollowing analysis.
The lack of reliable rent data is a common problem for empirical analyses based on Equation(1). In this study, for a consistent deﬁnition across 17 countries, we use working-age per-capita
real gross domestic product (GDP) as a proxy variable for real rent R. This treatment can bejustiﬁed as follows. If we consider GDP from the consumption side, the share of the household
consumption basket paid toward housing services is roughly 25%–30% in each country. Thus, if
we consider that households mainly comprise working-age people, using working-age per-capita
real GDP as a proxy variable for real rent R may be considered a reasonable assumption.*10
Meanwhile, as mentioned previously, Takáts (2012)[35] and Nishimura and Takáts (2012)[25]
derive the relationship between working-age population increases and rises in real residential
property price using a two-generation intergenerational model. Furthermore, empirical studies
such as Takáts (2012)[35] and Saita et al. (2016)[32] indicate that population composition has
a signiﬁcant impact on residential property prices. Based on the previous research’s ﬁndings,
we specify the expected change rate of housing rents as a function of population factors,
namely the population compositions and the total population. As we have clariﬁed, population
variables may not be accurately estimated, and their errors may persist and accumulate overtime (that is, they may not be “rational”). To incorporate these possibilities in the perfectforesight framework of Equation (1), we assume perfect foresight of demographic variables’
expectation errors and do not impose zero-sum constraints.
Equation (2) is a benchmark speciﬁcation derived by performing a logarithmic transforma-*7 We perform a robustness check based on the PVR using real residential property price, real rent, andreal interest, but there are no major changes in the basic results. The robustness check is performed
using both perfect foresight and static expectation for the real interest rate. For details, see Appendix
1.
*8 Walras (1954)[38] is the ﬁrst to model the PVR of asset prices. For further model details, see Campbell
and Shiller (1988)[2].
*9 In addition to the nominal interest rate there is a nominal risk premium in the denominator since
the residential property is a risky asset. Thus even if the nominal interest rate becomes negative, thedenominator is still positive and PVR is well-deﬁned. For simplicity, we assume the nominal risk premium
does not change over time and thus it becomes a constant in Equation (2).
*10 Chapter 6 (“Measuring the Services of Durables and Owner Occupied Housing”) in Diewert et al.
(2020)[8] presents the situation in various countries along with a housing services estimation method.

7

tion on both sides of the long-term PVR established based on the above:*11 *12
!
Ã
Yjt
rppi
cpi
+ β3 ijt
log Pjt = β0j + β1 log Pjt + β2 log
popwrk
jt
wrk
old
wrk
+ β4 log poptotal+ β5 (nyngjtjt − njt ) + β6 (njt − njt ) + εjt ,(2)where P rppi denotes the residential property price index, P cpi is the consumer price index, Y
is the real GDP, i is the nominal interest rate, poptotal is the total number of population, andnyng , nwrk , and nold are the shares of the total population that belongs to three generations,young (ages 0-14), working-age (15-64), and old (65+), respectively. The subscript j represents
the country, and t represents the time period. εjt denotes the disturbance term. Economic
theory expects the following restrictions in the coeﬃcients: β1 = 1 (absence of money illusion)，
β2 > 0 (an increase in housing rents raises residential property prices), and β3 < 0 (anincrease in the nominal rate of interest lowers residential property prices), as will be veriﬁed
below. In Takáts (2012)[35] and Nishimura and Takáts (2012)[25]’s two-generation model, themain buyers of property are the younger generation; therefore, it is predicted that increases
in the younger generation’s population will result in higher real residential property prices(β5 > 0). Conversely, it is expected that increases in the older generation’s population will
have a deﬂating eﬀect on residential property prices (β6 < 0).
In the long-run relation Equation (2), the constant term diﬀers by country, but we presume
that other variables’ coeﬃcients are homogenous, with no diﬀerences between countries, basedon the assumption that the no-arbitrage condition in the competitive equilibrium is common
to all capital markets. This assumption will also be tested as part of the empirical research.
As an extension of the basic model, we perform two types of analysis. First, for the property
bubble and collapse periods, we empirically analyze what kind of eﬀect population composition
has on the impact of interest rates on property prices. Speciﬁcally, we add the population
factor and interest rate interaction terms to the estimation model.
Nishimura (2016)[24] suggests the possibility that optimism induced by population bonuses
and expanded credit conditions typical of low-interest rates have a fairly synergistic eﬀect onproperty demand and property bubbles. A decline in nominal interest rates has large positive
impacts on property prices when population is young and growing. In contrast, the experiencesof Japan, the United States, and Ireland, following property booms, show that the eﬀect ofmonetary easing measures, such as lowering of nominal interest rates, is severely restricted incountries facing population onus (aging) periods.
To test whether the phenomenon observed in these three countries is simply a coincidence,
we estimate a model that adds nominal interest rate and population ratio interaction terms*11 As the relationship between real GDP and real rent per capita among the working-age population is notnecessarily linear, β1 is not necessarily 1. In actual empirical research, it is not 1.
*12 To understand population dynamics’ impact on fundamentals, we employ the following speciﬁcation,
based on Takáts (2012), Saita et al. (2016)[32], and Tamai et al. (2017)[37].
wrk + δ nold ).
Population factorsjt = δ0 log(poptotal) + (δ1 nyng
3 jt
jt
jt + δ2 njt

Population factors are categorized by generation (young generation, working generation, old generation).
Each category’s deﬁnition is explained below. Since the total of the population ratios by generation at atime point t is always 1, δ1 , δ2 , and δ3 cannot be estimated simultaneously. This is handled by imposing
the restriction δ1 + δ2 + δ3 = 0 (Fair and Dominguez, 1991[10]). That is, the formula is modiﬁed asfollows:
wrk
old
wrk
Population factorsjt = δ0 log(poptotal) + δ1 (nyngjtjt − njt ) + δ3 (njt − njt ).

8

to the model above. The following equation is the expanded long-run equilibrium relation:
!
Ã
Y
jt
rppi
cpi
+ β3 ijt + β4 log poptotallog Pjt= β0j + β1 log Pjt+ β2 log
jt
popwrk
jt
wrk
old
wrk
+ β5 (nyngjt − njt ) + β6 (njt − njt )
wrk
old
wrk
+ β7 ijt × (nyngjt − njt ) + β8 ijt × (njt − njt ) + εjt .

(3)

We will examine Equation (3)’s estimated coeﬃcient of i incorporating the interaction term
to see whether the population bonus period’s coeﬃcient is signiﬁcantly diﬀerent from that of
the onus period.
Our second analysis investigates the eﬀect of persistent demographic expectation errors on
the residential property price in the long-run equilibrium. Property is a durable good, andso it is diﬃcult for supply to adjust instantaneously to sudden ﬂuctuations in demand. The
adjustment may be possible but with a substantial cost. Therefore, we may assume that the
supply side supplies housing by predicting demand for a certain period in advance.
In this section, we explore the type of impact there will be on residential property prices
if the population prediction at a given time turns out to be wrong in a future period. We
examine how expectation errors change results of the benchmark case Equation (2) and theextention case Equation (3). To do this we decompose the young population ratio nyng
usedjt
in the regression analysis in terms of the ratio n̆yng
at
time
t
predictedz
years
before
(in
jt
yng
yng
the empirical analysis, z = 5) and the expectation error njt − n̆jt , which is the diﬀerence
between the actual and predicted number. A similar procedure is applied to the old population
ratio.
yng
yng
nyng
(4)
+ (nyng
jt = n̆jt
jt − n̆jt ).
|{z}
{z
}
|
error

predicted

The long-run relation is modiﬁed by plugging in the following analysis:
!
Ã
Y
jt
rppi
cpi
+ β3 ijt + β4 log poptotallog Pjt= β0j + β1 log Pjt+ β2 log
jt
popwrk
jt
wrk
old
wrk
+ β5 (n̆yng
jt − n̆jt ) + β6 (n̆jt − n̆jt )
yng
wrk
wrk
+ β7 {(nyngjt − n̆jt ) − (njt − n̆jt )}
old
wrk
wrk
+ β8 {(noldjt − n̆jt ) − (njt − n̆jt )}
wrk
old
wrk
+ β9 ijt × (n̆yng
jt − n̆jt ) + β10 ijt × (n̆jt − n̆jt )
yng
wrk
wrk
+ β11 ijt × {(nyngjt − n̆jt ) − (njt − n̆jt )}
wrk
old
wrk
+ β12 ijt × {(noldjt − n̆jt ) − (njt − n̆jt )} + εjt .

(5)This makes it possible to decompose and analyze the eﬀects of predictable and unpredictableparts of population ratios on residential property price.

3 Data and Methodology
3.1 DATA
Following the global ﬁnancial crisis in 2008, internationally comparable property price indexes have been developed, led by the IMF and the BIS, with participation from the United
9Nations and the OECD.*13 The study covers the 17 countries in the four regions indicatedbelow, for which it is possible to obtain BIS data. The international panel data cover a wide
range of countries, rather than just Western countries: three from Asia-Paciﬁc (Australia,
Japan, New Zealand), two from North America (Canada, the United States), 11 from Europe(Belgium, Switzerland, Germany, Denmark, France, the United Kingdom, Ireland, Italy, theNetherlands, Norway, Sweden) and one from Africa (South Africa) (see Table I). We conduct
the analysis using balanced panel data for these 17 countries over 46 years from 1974 to 2019.
We use the Residential Property Price Index (local currency denominated in nominal terms)
published by BIS for P rppi . As this index is published quarterly, we use the simple averagefor each year. For nominal interest rates, i, the main source is long-term interest rates fromOECD.Stat. However, as data for Denmark, Italy, Japan, Norway, and Sweden are missing forpart of the study period, percent per annum data on interest rates, government securities, andgovernment bonds obtained from the IFS are used as a substitute. We use values obtained byconverting these nominal interest rates (annual rates) into continuous compounded interest
rates in the regression analysis. For real GDP, Y , we use the real GDP (local currencyunit) published in the World Bank’s World Development Indicators (WDI). The CPI, P cpi , islikewise obtained from the WDI.
Table I Complete List of Countries/Regions in Our Sample
RegionCountry

RegionCountry

Asia-Paciﬁc (3)Australia (AU)Japan (JP)New Zealand (NZ)

Europe (11)America (2)Canada (CA)United States (US)Africa (1)South Africa (ZA)

Belgium (BE)Switzerland (CH)
Germany (DE)
Denmark (DK)France (FR)United Kingdom (GB)
Ireland (IE)
Italy (IT)Netherlands (NL)
Norway (NO)
Sweden (SE)For population-related variables, we aggregate population data by country and age cohort(obtained from the United Nations’ World Population Prospects database) into three generations, young (ages 0–14), working-age (15–64), and old (65+) for each country, and calculate
the population ratios with respect to the total population, nyng , nwrk , and nold . Total population data are also used as an explanatory variable, poptotal .
In Equation (4), a realized population ratio is decomposed into a predicted ratio of someinterval ago and a prediction error. The selection of this prediction interval is an empiricaldecision. To capture housing investment’s characteristics (time lag between planning andconstruction start/completion), we select a ﬁve-year prediction interval for this study. In theanalysis of Equations (2) and (3), we use panel data for 17 countries covering 46 years from1974 to 2019. However, because the United Nations’ country-level population projection data
*13 Led by the IMF and BIS and administered by Eurostat, a handbook was created to show the procedure forgenerating internationally comparable property price indexes. Two of this study’s authors participatedin this project. Based on the handbook, various national statistics oﬃces have developed property priceindexes as public statistics, recorded in a BIS database. For more on the development process andcreation method of internationally comparable property price indexes, see Diewert et al. (2020)[8].

10Table II Panel Unit Root Tests
Level
log P rppi
log P cpilog(Y /popwrk )ilog poptotal
nyng − nwrk
nold − nwrk

IPS W test
1st Diﬀerence−10.364∗∗∗−6.472∗∗∗−18.205∗∗∗−19.201∗∗∗−3.512∗∗∗−7.309∗∗∗−1.376∗−0.495−10.617∗∗∗
4.116
5.136
7.496
−11.978∗∗∗0.0824

ADF-Fisher testLevel
1st Diﬀerence
37.722
189.104∗∗∗
18.1784.621
12.576218.792∗∗∗
48.427∗178.237∗∗∗103.722∗∗∗343.452∗∗∗
363.352∗∗∗
68.326∗∗∗129.88∗∗∗46.837∗

Note: ∗∗∗ , ∗∗ , and ∗ indicate rejection of the null hypothesis at 1%, 5%, and 10%
signiﬁcance levels, respectively. Lag length is selected by Schwarz information
criteria. Andrews automatic bandwidth selection and Quadratic Spectral kernel
are used. All test regression includes individual eﬀects as the exogenous variable.
Test regression of log P cpi , nyng − nwrk , nold − nwrk add individual linear trends forthe level unit root tests. IPS indicates Im-Pesaran-Shin. ADF indicates augmented
Dickey-Fuller.

are available only from 1982, this inevitably results in the usable sample period of Equation(5) starting after 1982.*14 Accordingly, the analysis of Equation (5) is based on a 31-year
panel for 17 countries from 1989 to 2019.
To understand the nature of these aggregated data, we perform two panel unit root tests:
the Im–Pesaran–Shin (IPS) test and the Fisher–type augmented Dickey–Fuller (ADF–Fisher)
test (Im et al., 2003[15]). The test is performed based on the following regression model:∆yit = ρi yi,t−1 +piXθiL ∆yi,t−L + αi dt + εit .

(6)

L=1

Here, dt is a term representing the deterministic factors, such as a constant and a trend.
The null and alternative hypotheses are as follows:
H0 : ρi = 0 for all i vsH1 : ρi < 0 for at least one i

Thus, the null hypothesis assumes that all series are a non-stationary process, whereas thealternative assumes that a fraction of the series are stationary.
Here, we summarize the test results (see Table II). The IPS and ADF–Fisher tests reach
identical conclusions. Speciﬁcally, the test results show that the residential property price,working-age per-capita real GDP, nominal interest rate, and total population are integrated oforder I(1). In contrast, test results of the CPI are stationary of order I(0) with a constant andlinear time trend. By deﬁnition, population ratios should be stationary processes, but the test
*14 The United Nations publishes projections for individual countries along with the global population every

two years (with some exceptions). Projections are made in ﬁve-year intervals. To date, population
updates have been made in 1982，1984, 1988, 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006，
2008, 2010, and 2012. For each update, the United Nations publishes population projections in ﬁve-year
intervals (e.g., 1985, 1990, 1995, 2000, 2005, 2010, 2015, etc.). By using this data, it is possible tocalculate approximate predictions for each year based on linear interpolation. We, therefore, analyze theactual population values in relation to past predictions and prediction errors over a certain period. For
the method of calculating the ﬁve-year population ratio projections used in the analysis, see Appendix
A-3.

11

results are mixed, possibly due to the small sample.*15 Based on the IPS and ADF-Fisher tests,
the null hypothesis is rejected if the series is diﬀerenced, suggesting the possibility that I(0)and I(1) processes are mixed. In either case, it is acceptable to consider that the maximum
order of integration is 1 for all the variables used in this study. Due to this mixed orderof integration, the panel autoregressive distributed lag (ARDL) approach is an appropriate
framework for the following investigation.

3.2 METHODOLOGY
The procedure for panel cointegration relation testing and estimation is as follows. First,
we perform a panel cointegration test based on residuals by checking the stationarity of theresiduals and testing the presence of a cointegrating relation, where the null hypothesis is the“absence of a cointegrating relation.” Here, we use the Kao test and Pedroni test as representative tests (Kao, 1999[17]; Pedroni, 1999[27], 2004[28]). The Kao test assumes that all
cointegration vectors are common to each country. We assume the commonality of the discounted PVR (housing market no-arbitrage condition) across all countries; therefore, the Kaotest’s assumption is not impossible. However, since the commonality assumption is typicallyan extremely strong hypothesis, there is also a possibility that the cointegration vectors will be
non-homogenous. In that case, it may be considered inappropriate to apply the Kao test. In
comparison, the Pedroni test may be considered more generally representative than the Kao
test, since it permits cointegration vectors that vary by country. Using these in combination,
it is possible to empirically demonstrate whether the variables showing the discounted PVR
in Equation (1) are in a long-run equilibrium relation, or, at least, whether it is impossible
to observe a long-run relationship between the housing markets in the 17 countries covered inthis study (i.e., whether there is no cointegrating relation).
Next, we estimate the long-run relationship based on the panel ARDL approach (Pesaran
et al., 1999[30]):
q
p
X
X
′
Xi,t−j + εit .
(7)
δij
λij yi,t−j +yit = µi +
j=0

j=1

Equation (7) is a typical ARDL(p, q) model, where p is the maximum lag length of dependent
variable yit , and q is the maximum lag length of a vector of explanatory variables Xi,t . It is
technically possible to set diﬀerent lag orders for each country, but, for simplicity, we havechosen to use a common order.
Since Equation (7) includes I(1) variables, one can derive its error correction form as:∆yit = θi (yi,t−1 − βi′ Xi,t−1 ) +p−1Xλ∗ij ∆yi,t−j +

j=1

q−1
X

∗′
δij
∆Xi,t−j + µi + εit ,

(8)

j=0

which is called a mean group (MG) model. The ﬁrst term in the right-hand side of Equation (8)corresponds to the long-run equilibrium relationship, whereas the second and the third terms*15 As the population ratio variables have values that are restricted to interval [0, 1], by deﬁnition, they

are stationary processes. However, with panel unit root tests such as in this case, it is sometimes
not possible to reject local non-stationarity. This is convenient for estimating a long-run equilibrium
relation model that includes population ratios in the explanatory variables, which should be stationary
processes under normal circumstances, as in this study. While the applications diﬀer from the present
study, Pedroni (2007)[29] and Cavalcanti et al. (2011)[3] were also able to estimate panel cointegration
relations including ratio variables (speciﬁcally, investment-income ratios) since they demonstrated local
non-stationary processes.

12

capture the short-run adjustment
processes.
in Equationsand (8) arePp
Pq The parameters
Pq
P(7)
p
∗
associated as:θi = −(1 − j=1 λij ), βi = j=0 δij /(1 − k=0 λik ), λij = − m=j+1 λim , andPq∗δij= − m=j+1 δim . Note that all coeﬃcients vary by country. For example, the coeﬃcientθi in Equation (8) represents the speed of adjustment of equilibrium errors, and this speedof adjustment varies by country. If a long-run equilibrium relationship exists between thevariables, the sign for the coeﬃcient θi may be expected to be negative and statisticallysigniﬁcant. Given that the long-run equilibrium coeﬃcient or cointegration coeﬃcient βi also
varies by country, this speciﬁcation also permits variation in the coeﬃcients of the variablesin the levels included in the discounted PVR, such as the elasticity value (degree of money
illusion) of nominal residential property prices with respect to the CPI. Moreover, coeﬃcientsfor variables in diﬀerence expressing short-run adjustment vary by country. It may easily be
expected that if housing market structure/policy and consumer preferences vary, the short-run
adjustment process and correction of equilibrium errors will also vary by country.
It is worth examining if the theoretically predicted homogeneity restriction on the coeﬃcientof long-run relationship is valid. With regard to this, the pooled mean group (PMG) modelis estimated.
Pp−1
Pq−1 ∗′∆yit = θi (yi,t−1 − β ′ Xi,t−1 ) + j=1 λ∗ij ∆yi,t−j + j=0 δij∆Xi,t−j + µi + εit .
(9)
Since Equation (9) is a non-linear model in terms of the parameter imposing the restrictionof homogeneity on the cointegration coeﬃcients (βi′ = β ′ ), maximum likelihood estimation isused (Pesaran et al., 1999[30]). This restriction may, at ﬁrst glance, seem strong. However,for the 17 countries covered in the analysis, we believe that we can assume that the ﬁnancial conditions are homogenous based on the eﬀects of no-arbitrage because of international
capital ﬂow. Econometrically, suppose the true long-run equilibrium coeﬃcients are common
among the sample countries. In that case, the PMG estimates will be more eﬃcient than the
MG estimates, making them preferable for the estimation. Conversely, if the true long-run
equilibrium relation coeﬃcients vary by country, the PMG estimates will not be consistent,
but the MG estimates will be. Therefore, we verify this by performing a Hausman test on thenull hypothesis that the PMG model is more appropriate than the MG model, thereby testing
the merits of a formulation that imposes homogeneity on the long-run equilibrium.

4 Estimation Results
This section summarizes the analytical results of the benchmark model (Equation 2), thetwo panel cointegration tests, and various panel ARDL speciﬁcations. We also report theempirical results based on the interaction between demographic composition and interest rateand its eﬀect on the residential property price (Equation 3) and the impact of persistentdemographic expectation errors on the residential property price (Equation 5).

4.1 LONG-RUN EQUILIBRIUM RELATION ESTIMATION: STATISTICALLY SIGNIFICANT DEMOGRAPHIC FACTORSFirst, we consider the panel cointegration test of Equation (2). The Kao test rejects thenull hypothesis at the 1% level, indicating the presence of cointegration (see Table III). Furthermore, in the results using 7 types of test statistics based on Pedroni, the panel v test
and panel ADF test reject the null hypothesis that a cointegrating relation does not exist at
the standard level of signiﬁcance (see Table III). The group ADF test also rejects the null13

hypothesis at the 1% level.*16 Based on these, we conclude that, while some of the variables
comprising the PVR include I(1) processes, we cannot rule out a long-run relationship between
these variables.
Table IV shows the PMG model and MG model estimates of the long-run parameters using
panel data from 1974 to 2019 for the 17 countries.*17 At a glance, the coeﬃcients of the MGmodel are largely insigniﬁcant, whereas the coeﬃcients of the PMG model are signiﬁcant withexpected signs. As shown in the bottom of Table V, the Hausman test statistic is 10.53, and its
p value is 0.1042.*18 Therefore, for the housing markets of the countries covered in our analysis
at least, the null hypothesis cannot be rejected, and the results support the commonality of
the long-run equilibrium coeﬃcients between the housing markets. Based on these results, we
present the PMG model results below.
The analyses of the PMG model estimation results in Table IV are as follows. First, the CPI
coeﬃcient is approximately 1, suggesting the possibility that money illusion does not exist.
Second, the coeﬃcient for the working-age per-capita real GDP is 0.410. This is a housing rent
proxy variable, and the fact that this coeﬃcient is positive is consistent with the discounted
present value theory. Third, the estimated value of the impact of the nominal interest rate is−8.705, which is also signiﬁcant at the 1% level. This result is likewise consistent with thetheoretical prediction based on the present value model wherein interest rate increases will
hurt asset prices. Finally, and most importantly, with regard to population ratio coeﬃcients,
the coeﬃcient for the young population ratio is 5.579, whereas the coeﬃcient for the oldpopulation coeﬃcient is −5.705. These coeﬃcients are statistically signiﬁcant at the 1% level.
Thus, if other parameters are constant, a 1% increase in the young population ratio increases
Table III Panel Cointegration Tests
Kao test
ADF t

Statistic

Prob.

−6.914∗∗∗0.000

Pedroni tests: Within-dimension
Panel v
1.897∗∗
0.029
Panel ρ2.093
0.982
Panel PP
1.079
0.859
Panel ADF
−2.864∗∗∗0.002
Pedroni tests: Between-dimension
Group ρ3.572
0.999
Group PP
2.142
0.984
Group ADF
−2.914∗∗∗0.002
Note: ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance at 1%, 5%, and 10% levels, respectively. For Kao test: No deterministic trend. Lag length is 1, and the bandwidthis 2 with Bartlett Kernel. For Pedroni test: No deterministic trend. Automatic lag
length selection on SIC with a maximum lag of 2. Bandwidth is 2 with Bartlett
Kernel. PP indicates Phillips-Perron. ADF indicates augmented Dickey-Fuller.
*16 According to Pedroni (2004)[28], if the sample size in the time series dimension is less than 100, as inthis study, the group ADF test and panel ADF test have the greatest test power.

*17 The ARDL model’s lag order was taken as p = 2, q = 1, based on Schwarz information criteria (SIC).
*18 The test statistics here follow a chi-square distribution with 6 degrees of freedom based on the null

hypothesis.

14

Table IV Estimation Results of Baseline Model, Equation (2)Parameters
cpi

log P
log(Y /popwrk )ilog poptotal
nyng − nwrk
nold − nwrk
error correction term

β1
β2
β3
β4
β5
β6

PMG

MG

∗∗∗

1.080
0.410∗∗−8.705∗∗∗
1.153∗∗∗
5.579∗∗∗−5.705∗∗∗(0.102)(0.201)(1.038)(0.426)(0.853)(0.834)

0.023
0.845
−8.056∗∗1.745−8.3260.566(0.434)(1.213)(3.653)(1.697)(5.818)(4.522)−0.111∗∗∗(0.023)−0.309∗∗∗(0.038)

N
log L

782
1606.4

Hausman test
Statistic
p-value

782
1808.110.53
0.1042

Note: This table reports the estimate of long-run coeﬃcients and error-correction term.
The column labeled ”Parameters” corresponds to the parameters of Equation (2). Standard errors are in parentheses. ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance at 1%, 5%, and
10% levels, respectively. The lag of the autoregressive distributed lag model, p = 2 andq = 1, is selected by Schwarz information criteria. PMG indicates pooled mean group.
MP indicates mean group. The Hausman statistic refers to the test statistic on the longrun homogeneity restriction, examining if the PMG estimator should be preferred to the
MG estimator.

residential property prices by 5.579%; conversely, a 1% increase in the old population ratio
has an equivalent downward eﬀect on residential property prices.

4.2 LONG-RUN EQUILIBRIUM INTERACTION BETWEEN DEMOGRAPHICCOMPOSITION AND NOMINAL INTEREST RATESAs before, we perform a PMG estimation of Equation (3), based on the ARDL speciﬁcation.
The estimation results are as shown in Table V. The interest rate coeﬃcient is insigniﬁcant,but the interest rate and old population ratio interaction term coeﬃcient is signiﬁcant.
Due to the interaction terms in Equation (3), the impact of interest rate cuts on residential
property prices depends on the population composition conditions. To evaluate the magnitude
numerically, we derive the marginal eﬀect using the coeﬃcient estimates of Equation (3), as
follows.
First, deﬁne the average marginal eﬀect of interest rate change on residential property priceof country j over time such as∂ log Pjrppi= β3 + β7 nyng
− (β7 + β8 )nwrk+ β8 nold
j
j
j ,
∂ij

(10)

where nyng
, nwrk, and nold
are the historical averages for each population ratio in a givenjjjcountry j. Then, the total marginal eﬀect of interest rate change on residential property priceis
rppi∂ log Pjt
∂ log Pjrppi
yng
g
]
old
wrk
(11)
=
+ β7 ng
jt − (β7 + β8 )njt + β8 njt ,
∂ijt
∂ij
15

wherek = nk − nk for k = yng, wrk, and old
nf
jt
jt
j

Using the estimation results in Table V, Equations (10) is re-written as follows:\∂ log
Pjrppi+ 28.291 nold
− 19.765 nwrk
= 3.949 − 8.526 nyng
j
j ,
j
∂ij

(12)

Table VI shows the average marginal eﬀect of interest rate increases on property prices
by country, calculated based on the population ratio average values obtained for the sample
period (1974 to 2019) using Equation (12). The average population ratios for the 17 countries
during this period are 20.4% for the young population, 65.4% for the working-age population,and 14.1% for the old population. The average marginal eﬀect of interest rate increases
obtained by plugging in these values is the value at the bottom of Table VI, −6.738. This
result signiﬁes that a 1% interest rate cut raises property prices by around 6.738% on average,
which is somewhat smaller in scope than the result obtained with the benchmark model in
Section 4.1 (8.705%).
With regard to individual countries, in South Africa, where the average ratio for the young
population is markedly high at 35.6%, a 1% interest rate decrease increases property prices by
9.713%. Similarly, in Ireland, which has the next highest young population ratio (25.0%), theﬁgure is 7.646%, and in New Zealand, which has the third-highest ratio (23.3%), it is 7.565%;
therefore, the impact on the property market is considerable.
The opposite phenomenon occurs in countries with a high old population ratio. Amongthe sample countries, Sweden has the highest ratio at 17.6%, followed by Denmark (17.2%)
Table V Estimation Results for Model Including Interaction Terms, Equation (3)Parameters
cpi

log P
log(Y /popwrk )ilog poptotal
nyng − nwrk
nold − nwrk
i · (nyng − nwrk )i · (nold − nwrk )error correction term

β1
β2
β3
β4
β5
β6
β7
β8

PMG

MG

∗∗∗

1.053
0.602∗∗∗
3.949
1.402∗∗∗
6.262∗∗∗−6.207∗∗∗−8.52628.291∗∗(0.089)(0.190)(5.920)(0.414)(1.191)(0.924)(6.358)(11.699)

0.312
0.963
−29.4381.519−22.389∗∗
13.693158.237∗−134.716(0.278)(1.194)(86.637)(1.570)(10.728)(10.255)(91.106)(181.930)−0.130∗∗∗(0.023)−0.372∗∗∗(0.046)

N
log L

782
1638.3Hausman test
Statistic
p-value

782
1900.911.42
0.1789Note: This table reports the estimate of long-run coeﬃcients and error-correction term.
Standard errors are in parentheses. ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance at 1%, 5%, and
10% levels, respectively. The lag of the autoregressive distributed lag model, p = 2 andq = 1, is selected by Schwarz information criteria. PMG indicates pooled mean group.
MP indicates mean group. Hausman statistic is for testing the null hypothesis of PMG
as a correct speciﬁcation against MG.

16

Table VI Eﬀect of 1% Nominal Interest Rate Increase
historical average shares (%)
nyng
nwrk
nold

coeﬃcients ofinterest rate

AU
BE
CA
CH
DE
DK
FR
GB
IE
IT
JP
NL
NO
NZ
SE
US
ZA

21.8
18.2
19.8
17.4
15.9
18.5
20.0
19.2
25.0
16.7
17.3
19.1
19.9
23.3
18.2
21.5
35.6

66.2
65.7
68.0
67.3
66.9
65.7
64.4
64.8
63.9
66.2
66.6
67.1
64.7
65.0
64.2
65.9
60.0

11.9
16.1
12.2
15.3
17.2
15.8
15.6
16.0
11.2
17.1
16.1
13.8
15.4
11.7
17.6
12.6
4.4

−7.635−6.045−7.714−6.512−5.752−6.165−6.082−5.980−7.646−5.724−6.152−7.045−6.162−7.565−5.321−7.325−9.713

Average

20.4

65.4

14.1

−6.738

Note: The historical average share of generations are calculated by using the datafrom the UN’s World Population Prospects for the period from 1974 to 2019.
The average marginal eﬀect of interest rate change (the numbers in the rightmost
column) is calculated using Equation (10). AU: Australia, BE: Belgium, CA:
Canada, CH: Switzerland, DE: Germany, DK: Denmark, FR: France, GB: theUnited Kingdom, IE: Ireland, IT: Italy, JP: Japan, NL: Netherlands, NO: Norway,
NZ: New Zealand, SE: Sweden, US: the United States, ZA: South Africa.

and Italy (17.1%). In these countries, a 1% interest rate cut raises property prices only by
5.321% (in Sweden) to 5.752% (in Denmark), which is about half the extent of the increase inSouth Africa. These ﬁgures show the eﬀect of monetary easing calculated based on historical
averages.
The key takeaway is that divergence from historical averages further enhances the impact of
the above monetary measures on the property market. Using the estimates reported in Table
V, Equation (11) is re-written as:
\
rppi
\
∂ log
Pjt
∂ log
Pjrppi
yng
g
]
old
wrk
=
− 8.526ng
jt − 19.765njt + 28.291njt .
∂ijt
∂ij

(13)

yng
Equation (13) implies that an increase in the young age population ratio (ngjt > 0) enhances
the interest rate eﬀects (since β7 = −8.526 < 0), while an increase in the old age population
old > 0) reduces the interest rate eﬀects (since β = 28.291 > 0). In other words, popratio (ng8jtulation bonuses will considerably strengthen the positive eﬀect of interest rate cuts (monetary
expansion), while conversely, population onuses will considerably reduce the positive eﬀect ofinterest rate cuts. These ﬁndings strongly support the hypothesis of a strong interaction between population statistics and monetary policy proposed by Nishimura and Takáts (2012)[25]
and Nishimura (2016)[24].
174.3 PERSISTENT DEMOGRAPHIC EXPECTATION ERRORS AND LONG-RUN
EQUILIBRIUM
The estimation results of Equation (5) are summarized in Table VII.*19 There are changes
in the estimation values that are statistically signiﬁcant, such as the CPI coeﬃcient (1.386),
which is higher than the estimates in the previous sections, and the coeﬃcient for working-age
per-capita GDP almost doubling (from 0.410 to 0.973). Nonetheless, in each case, there isno qualitative change in the interpretation of these variables, except for the coeﬃcient for
the total population is negative. The shortened estimation interval may also have had aninﬂuence.
Equation (5) implies that marginal eﬀect of interest rate change on residential property
price of country j is:*20
rppi∂ log Pjt
wrk
old
= −1.886 − 33.013 n̆yng
jt − 7.001 n̆jt + 40.014 n̆jt
∂ijt
yng
wrk
wrk
− 413.758 (nyngjt − n̆jt ) − 105.990 (njt − n̆jt )old+ 519.748 (noldjt − n̆jt ).

(14)

Thus, marginal eﬀect of interest rate change has seven parts: constant, three predicted popuyng
yng
wrk
old
wrk
wrk
lation ratios n̆yng
jt , n̆jt , and n̆jt , and three prediction errors njt − n̆jt , njt − n̆jt , andoldnold
jt − n̆jt .
The second term of Equation (14) represents the change in residential property prices withrespect to the portion of the young population ratio increase that was predicted in advance.
The sign of the estimate, −33.013, suggests that interest rate cuts with an increase in thepredicted young population ratio cause additional upward pressure on residential property
prices, and the coeﬃcient is signiﬁcant at 10% level. In addition, the fourth term suggeststhat a predicted increase in the old population ratio decreases the residential property priceincreasing eﬀect of interest rate cuts even if they were predicted and their impact is statisticallysigniﬁcant. This result is consistent with our ﬁndings in the previous sections that population
onuses decrease the positive eﬀect on residential property prices.
Finally, and most importantly, we consider the impact of supply and demand mismatch
due to prediction errors based on the ﬁfth and seventh terms. As the sign of the coeﬃcientfor the young population ratio prediction error is negative, unforeseen increases in the young
population will amplify the eﬀect of interest rate cuts. Conversely, the sign is positive for old
population ratio-related prediction errors; therefore, if the aging of the population proceeds
more rapidly than expected, it will further decrease the eﬀect of interest rate cuts on increasing
residential property prices.
Furthermore, on comparing the prediction error coeﬃcients, we ﬁnd that old population(519.748) prediction errors have a greater impact than young population errors (−413.758)*19 p = 2, q = 1 was selected as the optimum lag length for ARDL, based on SIC.
*20 Using Equation (5), the marginal eﬀect of interest rate change on residential property price of country

j is derived as:
rppi∂ log Pjt
∂ijt

yng
yng
wrk
old
wrk
wrk
= β3 + β9 n̆yng
jt − (β9 + β10 )n̆jt + β10 n̆jt + β11 (njt − n̆jt ) − (β11 + β12 )(njt − n̆jt )old+β12 (noldjt − n̆jt ).

By substituting the corresponsing estimates from Table VII, Equation (14) is obtained.

18

Table VII Estimation Results for Model Including Population Prediction Errors, Equation (5)Parameters
cpi

log P
log(Y /popwrk )ilog poptotaln̆yng − n̆wrk
n̆old − n̆wrk(nyng − n̆yng ) − (nwrk − n̆wrk )(nold − n̆old ) − (nwrk − n̆wrk )i · (n̆yng − n̆wrk )i · (n̆old − n̆wrk )i · {(nyng − n̆yng ) − (nwrk − n̆wrk )}i · {(nold − n̆old ) − (nwrk − n̆wrk )}

β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12

error correction term

PMG
1.386∗∗∗
0.973∗∗∗−1.886−1.884∗∗19.374∗∗∗−8.630∗∗∗39.702∗∗∗−33.230∗∗∗−33.013∗40.014∗∗−413.758∗∗∗
519.748∗∗∗(0.273)(0.229)(9.764)(0.916)(2.759)(1.243)(4.554)(4.237)(17.989)(15.551)(48.649)(90.639)−0.092∗∗(0.042)

N
log L

527
1401.217

Note: This table reports the estimate of long-run coeﬃcients and error-correction
term. The column labeled ”Parameters” corresponds to the parameters of Equation (5). Standard errors are in parentheses. ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance
at 1%, 5%, and 10% levels, respectively. The lag of the autoregressive distributed
lag model, p = 2 and q = 1, is selected by Schwarz information criteria. PMG
indicates pooled mean group.

on the marginal eﬀect of interest rate cuts in absolute value. These implications of prediction
errors are likewise consistent with the analysis results in the previous sections.

5 Discussion: Demographics, Residential Property Prices, andCredit Conditions
In this study, focusing on residential property, which, as a means of wealth accumulation,
represents the largest share of household assets regardless of the country, we empirically clarify
the relationship between changes in demographics (including the aging of the population),nominal interest rates determined by monetary policy and residential property prices.*21 We
also ﬁnd the importance of demographic expectation formation: considerable diﬀerence exists
between expected and unexpected change in demography.
The large set of empirical analyses in Section 3 demonstrate that residential property pricechanges form a PVR in the long term and are determined as fundamental prices. Theseempirical ﬁndings reveal the relationship between residential property prices, demographics,
and nominal interest rates. Also we ﬁnd signiﬁcant diﬀerences among countries in the shortrun dynamics.*22 In this section, we once again verify the consistency of our ﬁndings with theexisting literature.
*21 We examine the case of real interest rates and real residential property prices in Appendix A-1, and ﬁnd

our resuts in Section 4 are robust.

*22 In Appendix A-2, we analyze accumulated responses of one unit shock to rents and interest rates, andshow siginiﬁcant diﬀerences among countries in the short-run dynamics.

19

First, in Section 4.1, we show that population factors are key variables for a PVR for longterm changes in residential property prices, based on long-term panel data covering a diverse
range of circumstances in 17 countries over 46 years. In other words, we ﬁnd that residential
property prices are determined by population composition ratios, in addition to working-age
per-capita GDP (a proxy variable for rents) and nominal interest rates. As most of thesevariables demonstrate unit root process characteristics, we conduct an analysis that treats thelong-term relationship between the variables as a cointegrating relation. In terms of speciﬁc
results, the study shows that if the ratio of the young population to the total population
rises by 1%, residential property prices will increase by 5.579%, while, conversely, if the oldpopulation ratio increases by 1%, residential property prices will fall by 5.705%.
Furthermore, in Section 4.2, we estimate the relationship to credit conditions during property bubble and collapse periods by adding a cross-term interest rate and population factors
to the model in Section 4.1. For example, in the case of Japan, whose property bubble thatstarted in the mid-1980s has been dubbed the biggest of the 20th century, baby boomers
entered the housing market in the early 1980s. They generated the most tremendous housing
demand in the country’s history, leading to a wave of excess optimism. Conversely, due to a
decline in the working-age population following the bubble’s collapse and then a decline in the
total population in the 21st century, excess pessimism became prevalent. The country hit aperiod of long-term economic stagnation known as the “lost decade.” When we consider the
Table VIII Marginal Eﬀect of Nominal Interest Rate i
predicted ratiosyngnnwrk nold

historical average (%)
prediction errors
yng
yng
n
− n̆
nwrk − n̆wrk nold − n̆old

coeﬃcients ofinterest rate

AU
BE
CA
CH
DE
DK
FR
GB
IE
IT
JP
NL
NO
NZ
SE
US
ZA

20.2
17.1
18.3
15.9
14.6
17.5
18.8
18.3
22.8
14.7
15.0
17.6
18.9
21.5
17.3
20.8
33.7

66.8
65.9
68.1
67.5
67.2
66.1
64.9
65.3
65.7
66.6
65.7
67.5
65.3
66.0
64.4
66.1
61.7

13.0
17.0
13.6
16.6
18.2
16.3
16.3
16.4
11.5
18.7
19.2
14.9
15.9
12.5
18.3
13.1
4.6

0.06
0.23
−0.12
0.32
0.11
0.15
0.09
0.05
−0.34
−0.23
−0.37
0.20
0.16
0.13
0.38
0.03
−0.70

−0.09
−0.20
0.18
0.14
−0.22
−0.16
−0.34
−0.19
0.50
−0.11
0.20
−0.17
0.02
−0.28
−0.20
−0.06
0.70

0.03
−0.03
−0.06
−0.47
0.11
0.02
0.25
0.14
−0.16
0.34
0.17
−0.02
−0.17
0.15
−0.18
0.02
0.00

−8.033−6.232−7.250−9.157−3.790−6.108−4.781−5.255−9.350−1.102−1.581−7.204−7.893−8.057−7.101−8.067−13.324

Average

19.0

65.9

15.1

0.01

−0.02

0.01

−6.723

Note: The historical average are calculated by using the data from the UN’s World Population
Prospects for the period from 1989 to 2019. The average marginal eﬀect of interest rate change,
the numbers in the rightmost column, are calculated by using Equation (14). AU: Australia,
BE: Belgium, CA: Canada, CH: Switzerland, DE: Germany, DK: Denmark, FR: France, GB:
the United Kingdom, IE: Ireland, IT: Italy, JP: Japan, NL: Netherlands, NO: Norway, NZ: New
Zealand, SE: Sweden, US: the United States, ZA: South Africa.

20results not only for Japan but also for the 17 countries over 46 years, we ﬁnd that the optimism caused by population bonuses and credit expansion conditions (typiﬁed by low-interest
rates) have a synergistic eﬀect on property demand and property bubbles as emphasized by
Nishimura (2016)[24]. Furthermore, we determine that the eﬀect of monetary easing measures,such as lowering of nominal interest rates, is severely restricted during population onus (aging)periods and in countries facing them.
As a criticism of various studies analyzing the relationship between demographics and the
housing market, starting with Mankiw and Weil (1989)[21], it has been pointed out that since
populations change only slowly if perfect foresight exists with regard to population changes andaging in the long term, price falls should not occur due to stock being adjusted through supply
adjustments (Engelhard and Poterba, 1991[9]; Hamilton, 1991[12]; Hendershott, 1991[13]).
However, if changes in the population composition are worse than forecast, deﬂation will
occur if production capacity adjustments (based on predictions) are too small. Therefore, in
Section 4.3, in response to these criticisms, we expand the model to include the eﬀect of thediﬀerence between population predictions and the actual populations (i.e., surprise) in various
countries on the residential property price inﬂation rate (deﬂation rate).
As expected, the obtained results show that unforeseen increases in the young population
ratio amplify the eﬀect of interest rate cuts and raise residential property prices. Meanwhile,the sign for prediction errors relating to the old population ratio in Equation (14) implies
that the aging of the population, which advances faster than expected, will curb the eﬀect ofinterest rate cuts in boosting residential property prices. The marginal eﬀects of increases ininterest rates on property prices by country, derived based on the population ratio averages
from 1989 to 2019, are presented in Table VIII.*23 Several interesting suggestions may beobtained from this table.
First, in the case of Australia and the United States, three average prediction errors areeﬀectively zero (or less than 0.1%), which shows that, while the possibility of errors occurring
at a given point during the period cannot be dismissed, in general, there is no bias in thepredictions. Therefore, in these two countries, the relationship between demographic changes
and interest rate cuts eﬀects may be determined by predictable factors (the second and thirdterms in Equation (14)).
Second, in Belgium, Canada, Denmark, the Netherlands, and South Africa, the average
old population ratio prediction errors are zero (or less than 0.1%), and there is no bias forthe period. Nonetheless, prediction errors occur for the young population, which enhances
the marginal impact of interest rate increases in the three European countries with positive
predictions errors and decreases it in the other two countries with negative ones.
Third, as for the countries with positive old population ratio prediction errors on average,
the marginal eﬀects of interest rate are as follows: Germany (average prediction error: 0.11%,
a marginal eﬀect: 3.790%), France (0.25%, 4.781%), the United Kingdom (0.14%, 5.255%),
Italy (0.34%, 1.102%), Japan (0.17%, 1.581%), and New Zealand (0.15%, 8.057%). Although
the marginal eﬀect is impacted by a combination of four population ratio factors and not by
old ratio prediction errors alone, the fact that the marginal eﬀect in ﬁve of these six countries(the exception being New Zealand) is signiﬁcantly below the overall average of 6.723%, may
be considered important in terms of the impact that population aging that exceeds predictions
has on monetary policy.
To summarize, both young population coeﬃcient signs are negative, while both old population coeﬃcient signs are positive, which is consistent with the series of estimation results andthe prediction results. Notably, among the two young population coeﬃcients, the prediction*23 The population ratios indicated in the table are the averages for the sample period.

21

error coeﬃcient is substantial. In comparison, interestingly, the prediction error coeﬃcient isalso very large among the two old population coeﬃcients. These results suggest that unforeseen changes in population composition have a considerable eﬀect on the impact of interest
rate cuts on property prices.
Results such as these also have implications concerning monetary policy. According to the
Taylor rule (Taylor, 1993[36]), when the economy is struggling (i.e., in times when the GDP
gap is negative), monetary policy shores up the economy by lowering interest rates. Whenthe economy is thriving (i.e., in times when the GDP gap is positive), excessive growth iscurbed by raising interest rates. However, this is not necessarily true for property prices
for all countries for all periods. Thus, the ﬁnding that the eﬀects of monetary policy are
related to population composition (e.g., the degree of population aging) in various countries
has important implications for policymakers.

6 Conclusion
From the estimation results of a large set of econometric models based on data of diverse
countires in Europe, Asia Paciﬁc, Africa and Americas, we reveal that ﬂuctuations in property
prices are determined by the PVR in the long run and are also strongly inﬂuenced by population dynamics. Focusing on these dynamics, we attest that during the “population bonus
period,” when the population and the proportion of the working-age population increased,resiendital property prices soared as housing demand increased. This tendency is strengthened further when credit conditions are loose with low nominal interest rates. Moreover, if
demographic changes are unanticipated, then the credit conditions’ eﬀects become larger. In
contrast, “population onus period”, when the portion of old population is increased substantially, residential property markets are stagnated, and looseing of credit conditions do nothave as strong positive eﬀects as in the case of population bonus period.
We also show that the interaction varies across countries between demographic factors andcredit conditions (nominal interest rates) determined by monetary policy. This result has animportant implication for policies: diﬀerent countries should have diﬀerent policies to counter
undesirable eﬀects of demographic changes and credit conditions on property prices.
However, some issues still prevail. First, in the current analysis, the deﬁnitions of workingage population and old population are ﬁxed and exogenous. In the future, increases in therate of capital accumulation through investment in residential property and decreases in therate of return could be slowed down to some degree due to workers deferring retirement. We
may incorporate retirement decision in deﬁning working age population.
Second, our model is based on the assumption of relatively homogeneous population. However, population has become heterogeneous as immigration/emigration is increasingly important. As population becomes heterogeneous, its compositional eﬀect may change over time.
Such change will be incorporated in our future reseach.
Third, there is another kind of heterogeneity with respect to property markets. In fact,bipolarization in residential property markets is under way: some parts of urban areas (socalled superstar cities) experience rapidly rising residential property prices while the rest of acountry suﬀers declining prices in regional property markets. Interestingly, some researchers
argue that aging population has caused this bipolarization or bifurcation of national property
markets. This is an important subject of future research.
Fourth, our model uses nominal interest rates describing credit conditions. However, in
recent years, there has been growing concern about the eﬀective lower band of nominal interest
rates, and central banks have been increasingly relying on quantitative easing. To incorporate
22

this unconventional policy is also important in future research.
Finally, this study is descriptive, and has not provided any suggestions concerning the issueof resource and welfare distribution. Previous research (Hirano and Yanagawa, 2017[14]) has
shown that productivity and economic growth rates do not return to their pre-bubble levels
due to the impact of property bubble formation and collapse on resource distribution. The
structure underlying this phenomenon could also have a linkage with demographics, which is
an issue we would like to examine in the future.

Appendix:A-1. Robustness Check: Analysis of Real Relationship
Theoretically, it is possible to interpret a discounted PVR as a long-run equilibrium relationship between real variables (Walras, 1954[38]). In this study, thus far, we have performed
empirical analysis using nominal residential property price and interest rate values. This isbecause, for real values, there are multiple deﬁnitions based on expectation formation hypotheses. Accordingly, in this appendix, to verify the robustness of the estimation results reported
in this study, we create real variables based on two types of expectation formation that appear
frequently in the empirical analysis and present the cointegration test and cointegration vector
estimation results based on the unit root tests for the benchmark model used in Section 4.1.
The explained variable is the real residential property price index realP rppi which is deﬂatedby the consumer price index (CPI), while the explanatory variables are the working-age percapita real gross domestic product (GDP), the real interest rate r，and population factors.*24
!
Ã
Y
jt
rppi
+ α2 rjt + population factorsjt + εjt .
log(realPjt) = µj + α1 log(A1)
popwrkjt
Here, the real interest rate rjt is deﬁned using the following two formulas:
cpi
SEReal interest rate based on static expectations (SE): rjt= ijt − ∆ log Pj,t.
cpi
PFReal interest rate based on perfect foresight (PF): rjt= ijt − ∆ log Pj,t+1.

Furthermore, population factors show an eﬀect corresponding to the real expected change
rate of housing rents.
First, we consider the panel unit root tests’ results. Table A1 summarizes the test results forthe three new real variables. The real interest rate based on static expectations is rSE , and thereal interest rate based on perfect foresight is rP F . By Im–Pesaran–Shin (IPS) and Fisher–
type augmented Dickey–Fuller (ADF–Fisher) tests, just as we did for the nominal variables,for real residential property prices and static expectation interest rates, the null hypothesis
may be rejected at the 1% signiﬁcance level for the ﬁrst diﬀerenced series. Meanwhile, for theperfect foresight interest rate, the null hypothesis is rejected before diﬀerencing. Thus, it isacceptable to consider the maximum order of integration for these three series to be 1.
Next, we perform cointegration tests, again using two types of tests. Assuming that the
cointegration vectors are homogenous, the Kao test rejects the null hypothesis that no cointegrating relation is present at the 1% level for both interest rate models (Table A2). Furthermore, with the Pedroni test, the null hypothesis is also rejected at the standard level*24 It is assumed that that expected inﬂation rate frequently used by market players is equal to the ex-post

inﬂation rate.

23

of signiﬁcance for the Panel ADF and Group ADF (Table A2). Judging by these results incombination, a cointegrating relation may be deemed to exist.
Finally, the PMG model’s long-term coeﬃcient estimation results are summarized in Table
A3. The coeﬃcient for working-age per-capita real GDP (a proxy variable for real rent) is
positive and consistent with the discounted PVR. However, the estimated value is approximately 2 with either model, which is rather high compared with the value with the nominalmodel (0.606). Next, although the real interest rate coeﬃcient is negative and statisticallysigniﬁcant for the static expectation case, it is positive and insigniﬁcant for the perfect foresight case. It reﬂects the diﬃculty of creating suitable real interest rate data based on annual
data. Meanwhile, the results obtained with regard to population ratios are the same as forthe nominal model.
Table A1 Panel Unit Root Test — Real Variables
Level
log realP rppi
rSE
rP F

IPS W test
1st Diﬀerence

2.491−2.605∗∗∗−7.439∗∗∗−11.272∗∗∗−28.315∗∗∗−28.405∗∗∗

ADF-Fisher testLevel
1st Diﬀerence
16.87655.795∗∗131.482∗∗∗

194.775∗∗∗
563.27∗∗∗553.03∗∗∗

Note: ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance at 1%, 5%, and 10% levels, respectively. Lag length is selected by Schwarz information criteria. Andrews automatic
bandwidth selection and Quadratic Spectral kernel are used. All test regression includes individual eﬀects as the exogenous variable. IPS indicates Im-Pesaran-Shin.
ADF indicates augmented Dickey-Fuller.

Table A2 Panel Cointegration Tests — Real Variables
Static Expectation
Statistic
Prob.

Perfect Foresight
Statistic
Prob.

−3.915∗∗∗0.000−4.302∗∗∗0.000

Pedroni tests: Within-dimension
Panel v
1.779∗∗
0.037
Panel ρ0.377
0.647
Panel PP−1.2620.103
Panel ADF
−3.279∗∗∗0.001

1.624∗
1.362
0.200−2.988∗∗∗

0.052
0.913
0.579
0.001

Pedroni tests: Between-dimension
Group ρ2.235
0.987
Group PP
0.353
0.638
Group ADF −2.516∗∗∗
0.006

3.253
1.956
−1.977∗∗

0.999
0.974
0.024

Kao test
ADF t

Note: ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance at 1%, 5%, and 10% levels, respectively. For Kao test: No deterministic trend. Lag length is 1, and the bandwidthis 2 with Bartlett Kernel. For Pedroni test: No deterministic trend. Automatic
lag length selection on Schwarz information criteria with a maximum lag of 2.
Bandwidth is 2 with Bartlett Kernel. PP indicates Phillips-Perron. ADF indicatesaugmented Dickey-Fuller.

24

Table A3 Estimation Results of Baseline Model with Real Residential Property Price
Static Expectation
wrk

∗∗∗

Perfect Foresight
1.885∗∗∗(0.134)(0.219)(0.698)(0.692)0.237
1.307∗∗∗
3.978∗∗∗−3.486∗∗∗(0.495)(0.224)(0.732)(0.686)(0.033)−0.166∗∗∗(0.034)log(Y /pop
)
rSE
rP F
log poptotal
nyng − nwrk
nold − nwrk

1.848
−1.044∗∗(0.118)(0.522)

1.045∗∗∗
3.160∗∗∗−3.315∗∗∗error correction term

−0.173∗∗∗

N
log L

782
1544.0765
1515.1

Hausman Test
Statistic
p-value

3.29
0.65463.45
0.6305

Note: This table reports the estimate of long-run coeﬃcients and error-correction
term. This table reports the estimation results by pooled mean group (PMG) estimator. Standard errors are in parentheses. ∗∗∗ , ∗∗ , and ∗ indicate the signiﬁcance
at 1%, 5%, and 10% levels, respectively. The lag of the autoregressive distributed
lag model, p = 2 and q = 1, is selected by Schwarz information criteria. For brevity,
the mean group (MG) estimation results are not reported. The Hausman statistic
refers to the test statistic on the long-run homogeneity restriction, examining if
the PMG estimator should be preferred to the MG estimator.

A-2. Residential Property Price Short-Run Adjustment Process
The analysis thus far has focused on the long-run equilibrium relation based on the discounted PVR. However, in the housing market, where transaction costs and information
asymmetry exist, it is diﬃcult to instantly realize the fundamental value. Therefore, based on
the PMG estimation results of Equation (9) in Section 4.1, we analyze the adjustment pathuntil residential property prices reach long-run equilibrium when an exogenous shock occurs
to residential property price fundamentals.
Using the estimates of common long-run parameters as well as the country-speciﬁc short-run
paramters of the PMG model, and by successive substitutions of Equation (9), it is possible
to express a residential property price of country j at time t as the sum of a deterministic
component, past fundamental factors, and residential property price shocks of its own. Hence,the eﬀect of a fundamental shock on the residential property price level can be obtained bycomparing two paths: one with a fundamental shock, and the other without a fundamental
shock.*25 Here, we investigate the eﬀects of two fundamental shocks: housing rent increases
and nominal interest rate drops. Note that we are using a single equation model, variables
other than the series giving the shock and the residential property price are assumed to beconstant.
First, we consider the reaction of residential property prices to housing rent shocks. Figure
A1 shows the accumulated eﬀect on residential property prices when the working-age per*25 For a similar analysis with a vector autoregressive (VAR) model including exogenous variables,

Lutkepohl (1993, p. 327)[20].

25

see

capita GDP increases by 1 unit. The horizontal axis is the number of years since the shock
occurred, while the vertical axis is the residential property price increase rate. Based on theassumption of a long-run adjustment process, the values are illustrated over three decades.*26
The ﬁrst characteristic is that the residential property price increase rate converges at around
0.4% over the long run. This is also the result expected based on the estimated long-run
equilibrium relationship of the benchmark model. However, the second characteristic is thatsigniﬁcant variation by country may be seen in the pattern of convergence to the long-run level.
For example, countries other than Australia exhibit a residential property price overshoot.
Moreover, the number of years required until the post-shock residential property price increase
reached a peak was two years for Canada, Denmark, and Ireland, three years for the United
Kingdom, the Netherlands, Norway, Sweden, and South Africa, four years for Belgium, France,
Germany, Italy, Japan, and New Zealand, and ﬁve years for the United States.
Among the G7 countries, the increase rate was highest in the United Kingdom, followed
in order by the United States, France, Italy, Canada, Germany, and Japan.*27 Increases inworking-age per-capita GDP directly produce housing demand and, therefore, the overshootobserved in the residential property price reaction may be considered an understandable phenomenon.
Next, we consider the decreasing eﬀect of nominal interest rates. Figure A2 illustrates theeﬀect of credit expansion, which is deﬁned as a 1% decrease in the nominal interest rate.
Switzerland, whose reaction path displayed divergent tendencies, is omitted from this graph.
In terms of characteristics that may be observed from the graph, residential property prices rosein 10 countries (Belgium, Canada, Denmark, the United Kingdom, Ireland, the Netherlands,
New Zealand, Sweden, the United States, and South Africa) immediately after the interest
rate cut, and in these 10 countries, the increase continued for at least four years. In the othersix countries, residential property prices decreased at ﬁrst immediately after the interest ratecut, but in four countries (the exceptions being Italy and Norway), they stopped decreasing
after one year, while in Italy and Norway, they stopped decreasing after two years.
On examining G7 countries in detail, we observe that the reaction diﬀers from housing rent
shocks. One notable characteristic compared to housing rent is that adjustment of residential
property prices in response to credit expansion requires a longer period. As the reduction ofinterest rates aﬀects information asymmetry between borrowers and lenders, the impact on
housing demand is indirect. It is therefore understandable that the reaction to interest ratecuts is slow.

A-3. Procedure for Creating Population Ratio Five-Year Prediction
Data
The United Nations publishes its revisions of the World Population Prospects every two
years (with some exceptions). To date, updates have been made in 1982, 1984, 1988, 1990,
1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, and 2012. Each revision publishes
population projections for years ending in 0 or 5 (i.e., 1985, 1990, 1995, 2000, 2005, 2010,
and 2015, among others). The table below shows predicted and actual values for the 0to-14-year-old population ratio in Australia, obtained from the revision reports.
*26 Among the 17 countries, Switzerland alone showed divergent behavior, and it was therefore excluded

from the ﬁgure.

*27 Since Figure A1 shows point estimates without conﬁdence intervals, caution is required when interpretingthe size magnitude.

26

(a) G7 Countries(b) 10 Non-G7 Countries (Excluding Switzerland)
Figure A1 Accumulated Responses of a Positive One Unit Shock to log(Y /popwrk ) on
Own log P rppi
Notes: The ﬁgure shows the reaction of nominal residential property prices in eachcountry to a 1-unit increase in working-age per-capita real gross domestic product.
Panel (a) is the reaction in G7 countries. Panel (b) shows the average for the 17 countries
and the reaction of nine other countries (Switzerland is excluded). For abbreviations
used in these ﬁgures, see Table I.

27

(a) G7 Countries(b) 10 Non-G7 Countries (Excluding Switzerland)
Figure A2 Accumulated Responses of a Negative One Unit Shock to i on Own log P rppi
Notes: The ﬁgure shows the reaction of nominal residential property prices in eachcountry to a 1-unit decrease in the nominal interest rate. Panel a is the reaction in G7
countries. Panel b shows the average for the 17 countries and the reaction of nine othercountries (Switzerland is excluded). For abbreviations used in these ﬁgures, see Table
I.

Column B is the predictions for 1985, 1990, 1995, and 2000 in the 1982 revision. Morelong-term predictions existed, but, for this study, data were collected by taking 20 years in
the future as the limit for long-term predictions. Past values relative to the 1982 update (e.g.,values as of 1980) are actual values, not predictions.
Based on these ﬁgures, approximate ﬁve-year predictions are calculated for all years in thesample period. The calculation methods for the three diﬀerent cases are explained below.
[1] For revision years ending in 0 or 528

Table A4 Predicted and Actual Values for the 0-to-14-year-old Population Ratio in Australia
A
1
2
3
4
5
6
7
8
9
10
11
12
13

1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035

B

C

D

E

F

G

H

I

J

K

L

1982
25.60
24.20
22.80
22.40
22.00

1984
25.30
23.60
22.50
22.20
21.60

1988

1990

1992

1994

1996

1998

2000

2002

2004

22.10
21.50
20.60
19.80
19.20
18.80

21.90
21.70
21.50
21.40
21.20
20.60

21.90
21.60
21.00

21.50
21.00
20.40
19.90
19.50
19.40

21.50
20.60
19.60
18.70
18.30
18.20

20.50
19.60
18.50
18.00
17.80
17.70

20.50
19.40
18.10
17.30
16.90
16.80

21.20
19.60
18.30
17.60
17.60
17.60

20.00

23.60
22.20
21.60
20.80
20.10
19.50

19.70
19.30

Note: For brevity, only a subset of revision years (columns of this table) and a part of published population
projections with ﬁve-year intervals (rows) are illustrated. For instance, the value of a cell B3 of this table(24.20) shows the predicted 0-to-14-year-old population ratio reported in the 1982 revision.

In this case, the ﬁve-year prediction published by the United Nations is used. For example, inthe 1990 revision, the prediction for 1995 is 21.5%. Therefore, we use this value as a ﬁve-year
prediction for year 1995 as of 1990.
[2] For revision years that do not end in 0 and 5
We calculate the ﬁve-year prediction through linear interpolation based on the published ﬁveyear-interval predictions. To explain this using the 1982 update as an example, the prediction
for 1987, ﬁve years after 1982, is calculated based on the predictions for 1985 (24.2) and 1990
(22.8) as follows: 24.2 + (22.8 − 24.2)/5 × 2 = 23.64.
Table A5 Prediction for Revision Years that Do Not End in 0 and 5, through Linear Interpolation
1
2
3
4
5
6
7
8
9
10
11
12
13

A

B

C

D

E

F

G

H

I

J

K

L

1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991

1982
25.60
25.32
25.04
24.76
24.48
24.20
23.92
23.64
23.36
23.08
22.80
22.72

1984
25.30
24.96
24.62
24.28
23.94
23.60
23.38
23.16
22.94
22.72
22.50
22.44

1988

1990

1992

1994

1996

1998

2000

2002

2004

23.60
23.32
23.04
22.76
22.48
22.20
22.08

22.10
21.98

21.90
21.86

21.90
21.84

Note: For brevity, only a subset of revision years (columns of this table) and a subset of predicted year (rows)
are illustrated.

Figure A3 below shows the predictions for Australia’s 0- to 14-year-old population ratio at
ﬁve-year intervals for each update year, calculated by employing linear interpolation using theabove method. The vertical axis is the proportion (%), while the variously colored lines show
diﬀerences by revision year.
29Figure A3 Predictions for Australia’s 0- to-14-Year-Old Population Ratio in Five-Year
Intervals by Update Year

[3] For Non-Revision Years
Predictions for non-revision years are obtained by performing linear interpolation using thepredictions from the previous and next revision years. The ﬁve-year prediction for 1988 as of1983 is obtained using the following method. First, the prediction for 1988 based on the 1982
revision is calculated as follows: 24.2 + (22.8 − 24.2)/5 × 3 = 23.36. Similarly, the prediction
for 1988 based on the 1984 revision is obtained thusly: 23.6 + (22.5 − 23.6)/5 × 3 = 22.94.
Next, the ﬁve-year prediction as of 1983 is obtained by performing linear interpolation of thesevalues for 1988: 23.15 = (23.36 + 22.94)/2.
Table A6 Predictions for Non-Revision Years Using Linear Interpolation
1
2
3
4
5
6
7
8
9
10
11
12
13

A

B

C

D

E

F

G

H

I

J

K

L

1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991

1982
25.60
25.32
25.04
24.76
24.48
24.20
23.92
23.64
23.36
23.08
22.80
22.72

1983
25.45
25.14
24.83
24.52
24.21
23.90
23.65
23.40
23.15
22.90
22.65
22.58

1984
25.30
24.96
24.62
24.28
23.94
23.60
23.38
23.16
22.94
22.72
22.50
22.44

1985

1986

1987

1988

1989

1990

1991

1992

23.60
23.37
23.13
22.90
22.66
22.43
22.35

23.60
23.35
23.10
22.85
22.60
22.35
22.26

23.60
23.34
23.07
22.81
22.54
22.28
22.17

22.20
22.08

22.15
22.03

22.10
21.98

22.00
21.92

21.90
21.86

Note: For brevity, only a subset of years (columns of this table) and a subset of predicted years (rows) areillustrated.

Using these methods, ﬁves-year projections are calculated for each year. The projection
value trends for the 65-and-over ratio for each update year obtained using a similar approach
are shown below.
30

Figure A4 Predictions for Australia’s 65-and-Over Population Ratio in Five-Year Intervals by Update Year

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