APIR Discussion Paper Series No.44
2016/9Population as a Source of Long−Term Growth:
From Malthus to Japan’s Postmodern Regime
Hayashi ToshihikoDirector for Research, Asia Pacific Institute of Research本稿の内容は全て執筆者の責任により執筆されたものであり、(財)アジア太平洋研究所の公式見解を示すものではない。

Population as a Source of Long−Term Growth: From Malthus to Japan’s Postmodern Regime
Toshihiko Hayashi1

Abstract This paper introduces a simple macroeconomic time series model incorporating a key concept of
GDP elasticity with respect to population (population elasticity). Using this model, we conducted empiricalanalyses of 158 countries each covering 25 to 180 years of history. As a result, we found first that the estimatedpopulation elasticity demarcated the countries according to regime, showing clearly whether a country was inthe ‘Malthusian regime’, in the ‘modern growth regime’ or in the ‘postmodern regime’. We found that the poorest countries as well as some oil-rich countries were in the Malthusian regime. The modern growth regime prevailed in most European, Asian and American countries in the 20th century. We then predicted long-term real
GDP for each country while they stayed in modern growth regimes. Third, we observed that both Germany andJapan went into a postmodern regime after a demographic transformation. Focusing on Japan, we argued that if
the nation remained in the modern growth regime, it would face a precipitous decline in GDP. We suggested thatJapan must reduce dependence on population as a source of growth in the postmodern era. This lesson might beimportant for the two thirds of countries in the world that are expected to enter a postmodern regime around the
middle of this century. (206 words)

Keywords population elasticity, Malthusian regime, JEL Classifications O11・O47・J11

1

hayashi-t@apir.or.jp
Director for Research, Asia Pacific Institute of Research, Grand Front Osaka C7, 3-1 Ofuka-cho, Kitaku, Osaka
530-0011, Japan1

Population as a Source of Long-Term Growth: From Malthus, through Modern Growth,
to Japan’s Postmodern Regime2
Introduction
Relationships between population and GDP have attracted many economists’ attention since the time ofThomas Robert Malthus. Galor and Weil (1999) reexamined this relationship and proposed a unified theoreticalmodel to characterize macroeconomic evolutionary stages from the Malthusian regime to the modern growth regime.
According to Galor and Weil, the Malthusian regime is the state of economy in which “technological progress
and population growth were glacial by modern standards, and income per capita was roughly constant” (Galor
and Weil (1999), p.806). They presented a dynamic theoretical model to illustrate that economies exit from theMalthusian trap and move into the post-Malthusian regime, and then to the modern growth regime.
Later research focused on how accelerated technological progress can foster demographic transitions, such asincreases in fertility rates and decreases in mortality rates. Lee (2003) talked about three centuries of fundamental change. Demographers’ research also focused on the impacts of GDP, GDP per capita and income on demographic variables, and showed how economic development changes demography.
On the relationship between population and the level of GDP, Huan and Xie (2013) conducted an empiricalanalysis taking the two-way effects between population growth and per capita GDP growth into consideration.
They used a sample of 90 countries covering the period 1980 to 2007 and found that population exerted negative
short-term effects on per capita GDP growth, but did not observe any reverse effects from GDP growth on population. Elgin and Tumen (2012) asked an increasingly important question: “Can sustained economic growth anddeclining population coexist?” They proposed a theoretical dynamic model in the optimal growth theory framework and answered this question in the affirmative. They also conducted empirical analysis to support their theoretical conclusion, analyzing a set of data that consisted of 50 countries and spanned the period from 1960 to2009. Another important contribution came from Prettner (2013) who looked into population aging in the context
of endogenous growth theory.
However, there has not been a comprehensive empirical study that examines the relationship between population and the level of GDP from a historical perspective. The purpose of this study is to do just that. First, we willbuild a simple auto-regressive model to estimate GDP elasticity with respect to population (population elasticity,
for short). We will find that population elasticity gives clear-cut quantitative definitions to the notions of ‘Malthus regime’, ‘modern growth regime’ and ‘postmodern regime’.
Second, we will predict how each country will fare in terms of GDP and per capita GDP while it stays in themodern growth regime. We will report our predictions for selected countries in this paper.
Third, we will focus on regime transformation from the modern growth regime to the postmodern regime.
What brings about this transformation is demographic transformation. Already Germany and Japan are in this2

Thanks are due to Mampei Hayashi and James Brady for helpful discussions, Jose O. TiuSonco II and Mizan
Bustanul Fuady Bisri for data assistance, and Miles Neale for editorial assistance. Financial assistance provided
by the Asia Pacific Institute of Research is gratefully acknowledged.

2

postmodern regime. We will focus on the Japanese case, and argue that reducing dependence on high population
elasticity will be necessary if the country is to maintain its moderately increasing per capita GDP. The lessons
that come from Japan’s regime transformation should be relevant to those two-thirds of countries that are expected to start losing population around the middle of this century.

Modeling Population and GDP
The Basic Model
A secular change in total population affects the aggregate supply and aggregate demand of the economy, in
addition to the political, social and institutional framework. On the demand side, effects will be felt in the overallhousehold consumption level as well as in the composition of consumption expenditures. Along with this, the aging of the population will increase household demand for health care, social security, pension services and otherrelated services. A change in population will also affect fiscal revenues, expenditures, exports and imports in national accounting.
On the supply side, we must recognize that population is the sole reservoir for labor supply, productivity,
management skill and new ideas and technologies. Coupled with policy efforts to improve human capital
productivity, population can change the overall efficiency of the economy, including that of the private and pub1

lic sectors. In other words, demographic change can affect the potential GDP of an economy .
The method most frequently used to assess contributions of factors of production is growth accounting. Using
historical records of GDP, which have been realized by the interplay of aggregate supply and aggregate demand,
growth accounting focuses on the contributions of stock of capital and labor input to the level of output. Typically, this approach assumes that the relationship between realized GDP, capital and labor inputs, and technologicalprogress can be described by a Cobb-Douglas function such that

,

where

stands for real GDP in year t,

for capital stock existing at the beginning of year t, andfor labor

input often measured in terms of work hours. α and β are capital and labor shares, respectively, when perfectcompetition prevails. When constant returns to scale is assumed,.

represents ‘total factor produc-

tivity’.
An extrapolative prediction of y can be obtained by calibrating new values for K and L using econometricallyestimated relative shares of capital and labor, and total factor productivity. Although this model is heavily used in
the literature, it presents economists with the critical difficulty of missing data when used to estimate the longterm structure of the economy. For example, the Penn World Table estimates data on stock of capital only back to1950. If we wish to apply the Cobb-Douglas formula over 140 years of history for example, the lack of data be-3

comes prohibitive.
However, we have a rich accumulation of data on population. Angus Maddison, in his seminal work (2008),
estimated historical population for more than 120 economies, from as far back as 1 AD for some of these. ‘UN
Population Prospects’ gives predictions for 160 economies up to 2100.
We will check if population is an effective predictor in a long-term analytical framework. For that purpose wewill modify the Cobb-Douglas function as follows:(1)

where yt-1 is substituted for Kt, andfor. Since we have a long series of data for y and P, this formulation

makes it possible to perform econometric estimations of the parameters.
Equation (1) is not without economic meaning. Consider a simple constant capital-output ratio model, whichsays

constant7. We can substitute, and letsubsume the constant capital-output ratio.

We will call β in equation (1) the ‘elasticity of GDP with respect to population’. In the short-term production
function, the power to labor supply is equal to labor’s share in GDP under perfect competition. However, we
would like to highlight the multi-channel effects of population on GDP, not just the contribution of labor supply
in the production process.
Also, notice that we are now using Xt instead of At. We would like to emphasize the importance of overall
productivity, or the ‘X-efficiency’, in a sense similar to the concept advanced by Leibenstein (1996).

A Fixed Effect Model
Empirical Model and Data
We will first estimate population elasticity for each economy. For the population data, we will rely on the
UN’s ‘Population Prospects’. Regarding GDP data, we will use the World Bank’s ‘World Development Indicators’ (WDI). In particular, we will use the series that presents GDP in US dollars (constant 2011 prices) converted by purchasing power parity, (NY.GDP.MKTP.PP.KD), over the period of 1990-2014.
In order to obtain a longer historical record, we will rely on the database compiled by Angus Maddison (AM),in which some series of yearly consecutive data go back to 1820. We will append the AM data to the WDI data2

and build a database of population and real GDP for 155 countries and regions covering 195 years .
As a starting point, we will employ a hypothesis that the X-efficiency is fixed over time for each economy.
This is tantamount to assuming that X-efficiency is a historically determined, economy-specific productivity
concept rooted deeply in the fundamental fabrics of the natural environment, culture and ethnicity of economies.
For empirical analyses, we will use a log transformed version of equation (1) such that,4

where j is a running index of economies. This is simply an auto-regressive model with the exogenous
variable3

Hence, we will run AR regressions for each economy for the period in which data are available .

Results of these regressions are summarized in the Appendix.
Population Elasticity and per capita GDP
Since

the rate of change in per capita GDP istimes the rate of change in population. Using this formula, we

can classify countries according to their population elasticity value and rate of population change as in Table 1.

Table 1: Population elasticity and growth regimes
RegimePopulation growth

Malthus<1+

Modern growth>1+

Postmodern growth<1-

The Malthusian regime is characterized by a population elasticity of less than unity and positive population
growth. In countries in this regime, population is increasing and per capita GDP is decreasing. The modern
growth regime emerges when both population and per capita GDP start to increase.
After the modern growth regime, population growth turns negative mainly because the fertility rate falls below
the mortality rate, and perhaps immigration plays a less important role in labor supply in the host country. If a
country’s population elasticity remains high in the face of declining population, per capita GDP will fall as a result. In the postmodern regime, an economy strives to reduce population elasticity while its population keeps declining, and it may end up with a mildly increasing per capita GDP if successful. This cycle may repeat itself in
future, although we have yet to observe such a phenomenon.

Three Development Regimes
The Malthusian Regime
First, let us look at our results for the economies that are in the Malthusian regime. We classified economies
that that showed Malthusian characteristics more than 25 times during the observation period as being in the regime. 13 economies fit our classification, showing these characteristics more than 25 times. We excluded fromour classification 23 additional countries that showed the characteristics less than 25 times. Most of the Malthu-

5sian regime countries are concentrated in Africa, the Caribbean and Central America. They belong to the lowincome country group according to the World Bank’s classification. These low income countries seem to typify
countries in the Malthusian regime. As an example, below is the scatter plot of ln(htpop) and ln(htgdppc) for
4

7.4

7.6

ln(htpoppc)
7.8

8

8.2

Haiti .

8

8.2

8.4

8.6
ln(htpop)

8.8

9

9.2

Figure 1: Haiti, 1945-2014,

Throughout the 70 years between 1945 and 2014, the Haitian population kept increasing without a break,whereas its per capita GDP fell persistently. The four dots at the south east corner correspond to the earthquakeof 2010, which claimed 160,000 lives, and the post-disaster recovery. A serious question for Haiti is whether it
can sustain the growth movement that started after the large-scale disaster.
Another example is the Central African Republic. This country experienced a chronic decline in per capita
GDP after declaring independence from France in 1960, while its population kept increasing. Since its independence the country has been plagued with political instability. The sharp drop that appears at the right-hand-most

6.4

6.6

ln(cfgdppc)
6.8

7

7.2

corner of the plot was caused by the political turmoil in 2013.

7.1

7.3

7.5

7.7

7.9
ln(cfpop)

8.1

8.3

8.5

Figure 2: Central African Republic, 1950-2014,

In addition, we found another category of countries with a population elasticity of less than unity. The countries in this category are Kuwait, Qatar and the United Arab Emirates. These are oil-rich economies with a per6

capita GDP exceeding 50 thousand current dollars each.
From 1950 to 2014, the UAE population increased 2.7 fold, Kuwait’s population increased 17.9 fold and in
5

Qatar, population increased 9.8 fold. In all these economies, population growth out-paced growth in real GDP .
6

These findings illuminate yet another dimension of the ‘resource curse’ paradox . Figure 3 and Figure 4 depict
the scatter diagrams of Kuwait and Qatar. Kuwait had a downward sloping scatter diagram for most of the 19502014 period. The ragged pattern that appears toward the right end is due to the military invasion by Iraq that

10

10.5

ln(kwgdppc)
11
11.5

12

12.5

started in 1990.

5

6

7

8

ln(kwpop)

Figure 3: Kuwait, 1950-2013, =0.60

Qatar was in the Malthusian regime between 1970 and 1993. During that period, it was an oil-producing
economy and its revenues were monopolized by the ruling monarch. In 1995, the son of the Emir overthrew hisfather in a bloodless coup, and since then it started on a modern growth path, changing its focus from oil and

11

11.5

ln(qagdppc)
12

12.5

13

natural gas to tourism and education.

3

4

5

6

7

8

ln(qapop)

Figure 4: Qatar, 1950-2014, =0.75

We may also note in passing that Russia showed an entirely different pattern. For Russia, GDP data is available only for 1990-2014, or 25 samples. Our AR estimation yielded a negative estimate for population elasticity.

7

10.2
10

2014

9.6

ln(rugdppc)
9.8

1990

1993
9.4

1998
11.87

11.88

11.89
ln(rupop)

11.9

11.91

Figure 5: Russia, 1990-2014, =-15.25

Figure 5 illustrates this. This scatter plot seems to show a negative correlation between ln(rupop) andln(rugdppc), a characteristic of a country in the Malthusian regime. However, the chronological order of eventsis different from previous cases. Russia’s population peaked off in 1993, and it has been declining ever since. In
other words, the plot line has moved from the lower right to the upper left in recent years.
In 1998, Russia experienced a financial crisis in the immediate aftermath of its transition from planned economy to market economy. GDP and per capita GDP started to increase after this crisis had subsided. However,
population kept declining during the recovery. We have recorded too few instances of relevant conditions toreach a conclusion on whether the Russian case suggests the existence of a Malthusian regime in reverse or apostmodern growth regime.
The Modern Growth Paradigm
In modern growth economies, population increases and per capita GDP rises simultaneously. Most of today’shigh-income and middle-income economies followed this pattern. Figure 6 and 7 illustrate two typical scatter

50

52ln(usgdppc)
54

56

58

plots: the United States from 1870 to 2014, and China from 1820 to 2014.

10.5

11

11.5

12

12.5

13

ln(uspop)

Figure 6: United States, 1870-2014, =2.23

The United States maintained growth in per capita GDP almost uninterruptedly for 144 years, with the excep-

8

tion of the World War II period. The war caused a sudden drop in the ratio of log of per capita GDP to log of
population, and a steep bounce-back in its immediate aftermath. The effect of WWII is visible in the middle ofthe scatter diagram.
What is prominent for China is that its growth in per capita GDP accelerated from around 1980, a rise that is
attributed to the launch of the ‘open door policy’ by Deng Xiaopin in 1978. China has become the second richest
country in the world in terms of GDP converted to US dollars at market rate of exchange, and its behavior affects,

67ln(cngdppc)
8

9

10

for better or for worse, the performance of many other national economies today.

13.2

13.4

13.6

13.8

14

14.2

ln(cnpop)

Figure 7: China, 1950-2014, =3.72

In fact, a majority of economies in the world entered into the modern growth regime in the 20th century, andupward rising scatter plots became a historical paradigm. How long does this paradigm last? We hypothesize thatan individual economy’s modern growth regime will last until the year in which a secular decline in the
population of said economy begins. We will now turn to long-term forecasts of GDP for countries and regions in
the modern growth regime.

Long-Term Forecasts for Countries within the Modern Growth Regime
G7 Countries, China and India
We tried to forecast future GDP to 2100 for countries for which we have obtained reasonably good estimates7of population elasticity . Figure 8 illustrates the predicted GDP trajectories of the United States, Canada, United
Kingdom, France, Italy, Germany and Japan (G7), and China and India. Notice that China, Japan, Germany, India and Italy are shown by truncated lines ending in varying years. This is because we predicted that the modern
growth regime would end at the point where the line ends for these countries. The United States, the United
Kingdom, France and Canada would keep their momentum as modern growth regime countries.
From Figure 8, we can make some interesting observations. First, although predicted GDP will have a confidence band, we predict the United States will stay on top of the world throughout the 21st century. Second, we

9predict that China will catch up with the United States around 2020, but will not supersede it before China’s
population starts to decline in 2028. Third, we predict that India’s GDP will keep growing until 2068, but will
stay below those of the United States and China. Fourth, we predict that France will grow faster than the United

GDP presdsicted on modern growth regime
27
25
28
29
30
31

Kingdom and Canada.

2000

2050
year
United States
FranceJapan

CanadaGermany
China

2100
United Kingdom
Italy
India

Figure 8: G7 Countries, China and India

On the other hand, the futures of China, India, Japan, Germany and Italy are difficult to predict. These countries will see their population peak before or within this century (China in 2028, India 2068, Japan 2009, Germany 1998 and Italy 2016), and will fall into the postmodern regime afterwards. Naturally, each economy will undergo a transformation to adapt to the phase in which the population declines. We cannot say with any
confidence how these economies can achieve growth in the postmodern regime. We will come back to this point
when we discuss the case of Japan in the next section.
Figure 9 illustrates how the nine countries will fare in terms of per capita GDP. Along the vertical axis, weare now measuring natural log of per capita GDP in international dollars at 2011 prices. As in Figure 8, truncatedlines indicate that those countries will undergo a regime change somewhere in the early 21st century. Based on
the results shown in Figure 9, we can classify the G7 countries, China and India into three groups. The firstgroup consists of the United States, Canada, France and the United Kingdom. These countries will steadily improve their per capita GDP following modern growth paths. Most prominently, France will supersede the UnitedStates around 2030 in terms of per capita GDP.

10

ln of per capita GDP in int'l dollars
29
30
31
32
28

2000

2050
year
United States
FranceJapan

2100

CanadaGermany
China

United Kingdom
Italy
India

Figure 9: Per capita GDP of the G7, China and India

Germany, Japan and Italy form the second group. Their per capita GDPs are more or less similar to the firstgroup of the most advanced counties at the start of the 21st century. However, how this second group will perform in terms of per capita GDP will depend on how they enter into the postmodern regime. The third group,
which includes China and India, will not be able to achieve the level of income that is currently attained in advanced economies. This observation raises two important questions for these countries: will they be able to escape from the middle-income trap and achieve sustained growth, and will they be able to construct a system of
welfare institutions before they face population decline?

Selected Asian Countries
South East Asia is one of the fast growing regions today. In fact, all countries in the region have escapedfrom low-income status and entered into the middle-income country group.8 However, some countries in the region, led by Thailand, Indonesia, Singapore, Hong Kong, Cambodia and Laos, will fall into the postmodern re-predicted GDP in ln billion int'l dollars
22
24
26
28
30

gime. Until that happens, the countries depicted in Figure 10 will keep growing in GDP.

2000
China
Philippines
Singapore

2050
year
Indonesia
ThailandHong Kong

2100
Viet Nam
Cambodia

Malaysia
Laos

Figure 10: GDP of Asian Countries

In terms of per capita GDP, Asian countries will keep their diversity. Singapore and Hong Kong will stay on
top, and Malaysia will follow. Thailand, China, Indonesia, the Philippines, Laos and Viet Nam will increase their11per capita income as a second group. For Cambodia and Myanmar (not shown in Figure 10), it will take consid-

32
31
30
29
28

ln of per capita GDP in int'l dollars

erable time before their living standards catch up with those of the other Asian countries.

2000

2050
year
China
Malaysia
CambodiaHong Kong

Indonesia
Philippines
Laos

2100
Viet Nam
ThailandSingapore

Figure 11: Per Capita GDP of Asian Countries

Selected African Countries
In Africa, South Africa is the largest economy. However, our prediction shows that South Africa’s GDP willmore or less stabilize before entering into the postmodern phase, and Republic of Tanzania and Equatorial Guin-22

ln of GDP in billion int'l dollars
24
26

28

ea will catch up with South Africa toward the latter half of this century, as Figure 12 illustrates.

2000

2050
year
Equatorial Guinea
Libya
Namibia
United Republic of Tanzania

2100
Gabon
BotswanaSouth Africa

Figure 12: Selected African Countries

In terms of per capita GDP, there is expected to be a big change in country rankings. Equatorial Guinea will be
the richest among seven countries, as illustrated in Figure 13. Botswana and Gabon will lift their per capita income steadily; Libya will be among the four countries that supersede South Africa if the state of civil war subsides. Tanzania will threaten the supremacy of South Africa in GDP, but will stay far below South Africa in percapita GDP.

12

ln of per capita GDP in int'l dollars
29
30
31
32
33
28
2000

2050
year

2100

Equatorial Guinea
Libya
Namibia
United Republic of Tanzania

Gabon
BotswanaSouth Africa

Figure 13: Per Capita GDP of Selected African Countries

The Richest and Poorest Countries Today
There will be a change in the order of the richest countries in the world in the near future. We chose to forecast the future growth of eleven countries that were richest in terms of per capita GDP in the World Bank ranking
in 2014. The most notable change is that the rankings of oil-rich countries like Qatar, the United Arab Emirates
and Kuwait will decrease. After 2060 they will not be the richest countries in the world any more. As Figure 14
illustrates, it will be Switzerland and Norway that come to the top. They will also be the fastest growing econo-

31

31.5

32

32.5

mies throughout the 21st century.

2000

2020

2040

2060

2080

2100

year
Qatar
UAE
IrelandSingapore
Switzerland
Bahrain

KuwaitHong Kong
Netherlands

NorwayUS

Figure 14: Today’s Richest Economies

Likewise, the poorest countries of today will diverge in economic development. Liberia will escape from its
poorest country status, but the standard of living in Niger, Madagascar, Malawi and Democratic Republic ofCongo will decrease still further. In all these countries in Africa, population will keep increasing.

13

30
29
28
27
26
2000

2020

2040

2060

2080

2100

year
Central Africa
MalawiTogo

Congo, D.R.
Madagascar
Guinea-Bissau

Liberia
GuineaComoros

Niger
Mozambique
Sierra-Leone

Figure 15: Today’s Poorest Economies

Postmodern Regime
Germany and Japan
Some economies, after reaching a certain level of development, started losing their population in the late 20thand the early 21st centuries due to many socio-economic factors, including a higher value of time, the proliferation of higher education, changes in people’s preferences and changes in social norms related to family and marriage. Two countries attract our attention in this respect: Germany and Japan.
Germany had a growing population and a gradually increasing per capita GDP until 1998. After 1998, as Figure 16 shows, Germany’s population started to decrease. However, Germany’s per capita GDP kept rising until
2013 with a brief decline in 2009, which was the year of the worldwide Great Recession. It may be hypothesized

31.2

31.4

that Germany entered the postmodern growth regime after 1998.

1998

degdppc
31

1984

30.6

30.8

1973

11.24

11.26

11.28
depop

Figure 16: Germany, 1967-2014;

11.3

11.32

over 1850-2013

Japan offers yet another example of an emerging postmodern growth regime. It followed the modern growth
regime until 2009, when a switch to the postmodern growth regime seems to have taken place. Again, the drop
appearing in the north-east corner of the graph corresponds to the Great Recession of 2009, the downturn that
followed a period of financial turmoil symbolized by the Lehman Brothers’ demise.

14

Will postmodern growth be sustainable? Will there be a reversal of the trend in which a population decline is

31.2

followed by a fall in per capita GDP in years to come?

30.9

31

jpgdppc

31.1

2009

11.7

11.72

11.74

11.76

jppop

Figure 17: Japan, 1988-2014;

over 1870-2014

Two-Thirds of Economies Will Follow
From here we will focus on Japan’s case. Before going into detail, we should confirm that the postmodern regime is not an anomaly confined to Germany and Japan. In fact, almost all economies in the world experienced
population growth throughout the 20th century, with the exception of Russia and Germany. However in the 21st
century, 157 economies, or 67.4% of countries and regions listed in the UN Population Prospects, will reach a
population peak and experience a subsequent continuous population decline toward 2100. If population increase
was prevalent throughout the world in the 20th century, population decline will be a new normalcy in the 21st
century.

9

Table 2 lists selected economies that show a higher rate of population decline. Russia, Ukraine, Romania and
Poland are projected to face the largest rate of decline as a country. Asian economies such as Thailand, Japan,
Korea and Nepal will face a rate of decline in the order of -0.05% per annum. Latin American economies like
Mexico, Brazil and Chile are no exception. Their population is forecasted to decline at -0.3% from the middle ofthe century.

Table 2: Rate of Population Decline
EconomyPeak (Year)

Rate of Decline (%)

Romania

19,511 (2015)-0.70

Thailand

68,673 (2023)-0.65

Poland38,812 (2015)-0.64

Ukraine44,824 (2015)

-0.62

Iran

92,261 (2048)

-0.54

Nepal

36,458 (2058)

-0.49

Korea

57,715 (2035)-0.48Japan*

127,341 (2008)

-0.46

15

Russia

148,436 (1993)-0.22

Germany
82,010 (1998)-0.02
Note: Rate of decline is calculated for the period from the peak to 2100 for each economy.

A Closer Look at Japan
So far we have used UN data and Maddison data for population, and World Economic Indicators andMaddison data for real GDP. The main reason we chose these GDP figures was because we wanted to constructreal GDP series that are internationally comparable. We also made this choice to avoid the ‘double conversion’problem posed by exchange rate conversion and constant prices conversion.
However, because we used that very method, our GDP data contained purchasing power parity conversion,
which is unnecessary for individual countries. Thus, we will use another set of data for our next investigation:
historically estimated and contemporarily compiled government statistics on Japan’s real GDP, expressed interms of local currency. Furthermore, we will use another source of population data independently estimated by aJapanese government-affiliated research institute.
IPSS Data on Japan’s Population
In ‘UN Population Prospects: 2015 Revision’, Japan’s population in 2100 is estimated at 83.175 million, downfrom the figure of 127.341 million estimated in the 2009 edition. Japan’s National Institute for Population andSocial Security Research (IPSS, 2014) estimated that the Japanese population would be 49.591 million in 2100,
with a peak of 128.057 million in 2010. Numbers differ between the two forecasts due to a difference in assumptions regarding fertility rate and mortality rate. But declines like 35% or 61% over a 90-year period are unprece10

dented in world history. We will call this change in Japan’s population the ‘great demographic transformation’ .
Regarding the historical statistics on Japan’s population, we will use in this section the official statistics of thegovernment and the population forecasts made by IPSS.
The government statistics were first recorded by the Bank of Japan (1960). They start from 1872 and are connected to the current data compiled by the Ministry of Internal Affairs and Communications. Population forecasts are provided by the IPSS based on assumptions regarding prospective birthrates and mortality rates. We
will use the historical data up to 2013 and IPSS’s forecasts based on a medium birthrate and medium mortality
11

rate for 2014 to 2100 . We will call the combined long-term population series jppop4.
A caveat is in order. The two series, namely AM+UN (which we used in the sections above) and jppop4, coincide for most of the historical period 1872 to 2013, but they diverge considerably in terms of future forecasts.
jppop4 gives a more pessimistic forecast than AM+UN, and the gap widens increasingly toward 2100.
The GDP Data
In recent years, the Cabinet Office has compiled official statistics for real GDP. Its postwar series starts from1955 and comes in three sub-series with different base years. We first constructed a chained series using the subseries with 2005 prices.

16

Historical data on real GDP are fragmented. Hitotsubashi University dedicated decades to estimating historicalseries on basic economic data including real GDP going back to 1878. The Ohkawa estimate is the earliest andthe most definitive estimate for the period 1878 to 1942 (Ohkawa, K, 1957). The Economic Planning Agency
published GNP series together with the GNP deflator in billion yen units from 1930 to 1964. We chained these
historical series and the postwar data to construct jpgdp4 in billion yen at 2005 prices, creating a set of data that
12

covers the period 1878 to 2013 .
A Model with Time Trend
So far, we have been using equation (1) with the assumption that the X-efficiency is specific to the country
concerned and is time invariant. However, in this section we assume that the X-efficiency is composed of a constant and a time trend. The equation to be estimated becomes.

(2)

Using this model, we can clarify the characteristics of Japan’s growth pattern in the prewar period (1878-1944),
the postwar period (1945-2015) and the modern growth period (1878-2009). The next table summarizes our results.

Table 3: Estimates of Prewar, Postwar and Modern Growth Data
(1) Prewar(2) Postwar(3) Modern growthyear
lnjppop4_cons

lnjpgdp4

lnjpgdp4

lnjpgdp4

1878-1944

1945-2015

1878-2010

0.036**

0.007

0.006

(3.12)(1.03)(0.65)

0.578

4.643

***

3.541***(0.56)(21.79)(6.18)-66.032***-55.173***-41.403**(-6.00)(-4.48)(-2.68)0.522***

0.959***

0.952***(4.06)(25.78)(29.69)0.084***

0.042***

0.078***(13.70)(17.09)(20.64)

67

71

ARMA
L.ar
sigma
_cons
N

BIC
-120.47-224.82
Notes: 1. z statistics in parentheses
2. * p < 0.05, ** p < 0.01, *** p < 0.001

133-273.24Comparing the results for prewar and postwar periods, we notice that the growth rate of X-efficiency was17much greater in the prewar period than in the postwar period, and in contrast, population elasticity was muchhigher in the postwar growth than in the prewar period. Simply put, the prewar modernization and growth of theJapanese economy largely originated from fast growth in X-efficiency. On the other hand, Japan’s postwar
growth, including the legendary high growth epoch of 1950-1973, was enabled by the nation’s high population
elasticity. Throughout the 133 years Japan spent in the modern growth regime, which included wars, social transformations, political turmoil and technological progress, the annual growth rate of X-efficiency was 0.6% andpopulation elasticity was 3.5.
GDP Prediction Based on Past Trends
A great concern in academia as well as in policy circles is how the Japanese economy will fare when population declines chronically. In policy discussions, many economists and institutions offer long-term forecasts ofGDP. The OECD (2014) provides the most comprehensive long-term forecasts for member countries, including
Japan. One of their concerns in relation to long-term forecasts of macroeconomic performance was population
aging rather than the level of population itself.
They pay attention to the possibility that the working age population will decrease by 7% in the OECD from2010 to 2060, whereas the total population of the OECD will increase by 17% 3. We argue that total population
matters more when it comes to long-term projections, especially for a country like Japan which is already witnessing a declining population.
In order to see what the future will entail for a Japan with a declining population, we predicted GDP based onlong-term estimates of the two parametersandlisted in the column (3) in Table 3. This is a prediction basedon the assumption that the structure of the economy, which has remained the same for the past 133 years, will be

10

ln of GDP in billion yen at 2005 prices
11
12
13

unchanged for another 90 years.

1950

2000

2050

2100

year
Historical GDP

GDP predicted on modern growth regime

Figure 18: Japan’s Historical GDP and its Predicted PathOur prediction shows a clear downward trend in Japan’s future GDP. The average annual rate of decline
comes to almost 3% from 2010 to 2100, or a drop from 512 trillion yen in 2010 to 257 trillion yen in 2100.
However, this prediction ignores the fact that the Japanese economy has been in the postmodern era since 2010.
A once-in-130-year demographic transformation is taking place. Whatever evolution Japan witnessed in the long18

period in which population trended upwards will not be repeated in reverse in a new phase in which secular population declines. What we need is not predictions based on past trends but simulations of what the future mightentail. We need to ask ourselves whether the simulated future path is feasible or realizable.
Some Simulations
To clarify this point, we ran some simulations. We considered alternative targets for GDP prospects. First, we
assumed that GDP would grow at the rate n% after 2015. We tried 0% growth (lnjpgdp40) and 1% growth(lnjpgdp41) as examples. Second, we examined what is needed to sustain 0% growth in per capita GDP(lnjpgdp400) and 1% growth in per capita GDP after 2015 (lnjpgdp401). The time paths corresponding to thefour different scenarios are represented in Figure 19. All scenarios are expressed in terms of ln of GDP in billion
yen at 2005 prices.
As is clear from Figure 19, the 1% GDP growth path is the most ambitious target compared to our predic13

tions based on the past 133 years of modern growth history . The 1% per capita growth trajectory behaves similarly to the 0% GDP growth path, which is natural since the rate of decline in population is approximately 1%

10

ln of GDP in billion yen at 2005 prices
11
12
13
14

per year.

2020

2040

2060
year

2080

2100

1% GDP growth
0% GDP growth
0% per capita GDP growth
1% per capita GDP growth
GDP predicted on modern growth regime

Figure 19: Predicted and Simulated Growth of Japan’s GDP

We next examined what combination ofandwould be able to bring about these paths. To find these, wehave only to run the same ARIMA regression on the simulated GDP series. Table 4 summarizes the results ofthese regressions.

Table 4: Estimation Results for Simulated Paths

year
lnjppop4

(1)

(2)

(3)

(4)

(5)

(6)

lnjpgdp4

lnjpgdp40

lnjpgdp41

lnjpgdp400

lnjpgdp401

lnjpgdp402

1878-20102010-2100

2010-2100

2010-2100

2010-2100

2010-2100

*

0.006

0.002

(0.65)(2.08)

3.541

***

0.150

0.002

0.010

***

0.016***(94.13)(1.79)(111.00)(7.53)

0.010

***

***

0.680***

0.010

***

19

1.191

0.980

(6.18)_cons-41.403(1.73)
**

7.684

**

(0.84)-7.219(11.22)(103.33)***-5.564-17.880***(3.79)-26.670***(-2.68)(2.80)(-20.57)(-1.45)(-62.70)(-4.46)

0.952***

0.939***

0.162*

0.957***

0.255***

0.972***(29.69)(31.02)(2.41)(32.88)(4.46)(21.88)0.078***

0.002***

0.001***

0.002***

0.002***

0.003***(20.64)(22.65)(24.31)(18.99)(25.49)(7.75)

133

91

91

91

91

91

-822.37-889.65-772.50

ARMA
L.ar
sigma
_cons
N

BIC
-273.24-828.10-914.55
Notes: 1. z statistics in parentheses
2. * p < 0.05, ** p < 0.01, *** p < 0.001

We can infer by comparison the plausibility of attaining each scenario. The 1% GDP growth scenario looks to
be close to impossible. For such a scenario to materialize, the annual rate of X-efficiency increase would have to
be more than triple the historical trend, and population elasticity would have to be halved from the historical
trend or cut by 64% from the postwar trend.
Would it then be feasible to sustain GDP at the 2015 level? Again, to achieve this, the growth rate of Xefficiency would have to be tripled, and population elasticity would need to be lowered considerably. Such a
drastic change is historically unprecedented and would seemingly be extremely hard to come by.
Then, what about keeping per capita GDP on a 0% growth path? Among the four scenarios, this looks to be
the most realistic one. Indeed

would have to be triple the postwar historical trend, andwould still beconsiderably lower than the 133 year trend.
In any case, a decline, not growth, looks inevitable for a Japanese economy with a declining population. The
most realistic choices seem to be either to keep the pace of overall change at the postwar historical level and accept a 0.47% annual decline in per capita GDP (and a 3% annual decline in GDP), or accelerate social change tosteer to a 2% increase in per capita GDP.
We can summarize our findings as follows:
1)

Japan’s GDP elasticity with respect to population was so high in the postwar period that most of the nation’s growth, including the historic high-growth epoch, can in fact be accounted for by population increase
alone. In this sense the ‘population bonus hypothesis’ applies to the Japanese experience.

2)

Such being the case, when Japanese population started to decline after 2010, a negative effect set in on Japan’s GDP as the postwar regime remained intact. Population became an onus on the economy. This will
become conspicuous after 2018.

3)

However, from the Meiji era to the Heisei era, the growth of the Japanese economy was dependent less onelasticity with respect to total population and more on growth in X-efficiency. We may call the structure of
the economy pertaining to these 133 years of history (encompassing political transformations, industrial
revolutions, wars, technological progress, and changes in the composition of output) the basso continuo of20

the Japanese economy.
4)

Playing this basso continuo into the future would only serve to set Japan’s GDP on a downward path, with
the nation’s population declining. Even if Japan does sustain 1% growth in per capita GDP, considerable efforts will have to be expended transforming social infrastructure and enhancing aggregate supply and demand to maintain the nation’s GDP growth.

Concluding Remarks
In this paper, we introduced a key concept of GDP elasticity with respect to population, or ‘population elasticity’ for short. In order to estimate empirically the degree of elasticity for individual economies, we proposedusing a simple ARIMA model to avoid the spurious correlation that would result from an OLS model and to incorporate the sequential dynamism built in to the population and GDP nexus. Using this model, we estimatedpopulation elasticity for 158 countries over a historical period from the earliest point recorded in the AM dataset
until 2014.
Based on our estimates of elasticity, we classified economies as being in one of three developmental stages:
the Malthusian regime, the modern growth regime or the postmodern regime. One of the important findings wemade in the classification process was that some high-income, oil-rich economies were in the Malthusian regime
until 2014.
Next, we used the aforementioned ARIMA model to make estimates of future population elasticity up until
2100, which yielded interesting non-linear predictions for individual economies. We showed that the UnitedStates, Canada, the United Kingdom and France would continue on a modern growth trajectory to 2100. We also
showed predicted GDP and per capita GDP for selected countries, with our predictions extending to the year
when each country enters the postmodern regime. In Germany, Italy and Japan, the postmodern regime has already started. This led to our next investigation.
In this investigation, we focused on the case of Japan as a forerunner. We used domestic data for GDP and
population to avoid complications arising from currency conversion. We also employed a hypothesis that Xefficiency growth consists of a time trend and an intrinsic constant. Even with this change, our post-estimation
prediction suggested that a decline in GDP was imminent for Japan.
Finally, we turned to an analysis of certain scenarios. We suggested various scenarios of growth in Japan’s
postmodern regime, and investigated what combination of parameters would bring those scenarios into reality.
We found that the scenario of 0% GDP growth and 1% growth in per capita GDP looked most plausible.
Although there are only a few years of data from countries in the postmodern regime that we can observe,
statistical inference based on old regimes would be grossly misleading. A method similar to the one we used inour scenario analysis must be developed for each country before two-thirds of countries fall into the postmodern
regime.

21

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Appendix: AR Regression Results
Eastern Africa

CodeElasticity（β） L..1（γ）

BIC

N

PeriodBurundibi

1.16***

0.96***-188.65

65

1950-2014

Comoroskm

0.98***

0.94***-153.8365

1950-2014

Djibouti

dj

0.69***

0.97***-167.8365

1950-2014

Ethiopia

et1.43***

0.98***-208.34

65

1950-2014

Kenya

ke

1.30***

0.86***-221.0165

1950-2014

Madagascar

mg

0.66***

0.93***-223.70

65

1950-2014

Malawimw

1.47***

0.92***-196.9165

1950-2014

Mauritiusmu

2.44**

0.99***-181.9765

1950-2014

Mozambiquemz

1.64***

0.97***-169.68

65

1950-2014

Rwandarw

1.50***

0.79***-101.0765

1950-2014

Seychellessc

2.56***

0.86***-195.2665

1950-2014

Somalia*so0.75***

0.72***-129.4359

1950-2008

Ugandaug

1.29***

0.98***-205.8565

1950-2014

United Republic of Tanzaniatz

1.34***

0.97***-255.0165

1950-2014

Zambiazm

1.21**

0.96***-183.0165

1950-2014

Zimbabwe

zw

1.22*

0.97***-155.40

65

1950-2014

Middle Africa

Code

BIC

N

PeriodElasticity（β） L..1（γ）

Angola*ao

0.88

0.95***-64.8559

1952-2008

Camerooncm

1.27***

0.96***-222.35

65

1950-2014

Central African Republiccf

0.60***

0.88***-155.0765

1950-2014

Chad

td

1.26***

0.94***-132.9665

1950-2014

Democratic Republic of the Congo

cd

0.51*

0.97***-165.1965

1950-2014

Equatorial Guinea

gq

2.82***

0.99***-33.4865

1950-2014

Gabon

ga

1.16*

0.96***-111.6165

1950-2014

Sao Tome and Principest

1.66***

0.96***-146.9365

1950-2014

BIC

N

PeriodNorthern Africa

CodeElasticity（β） L..1（γ）

Algeriadz

1.69***

0.88***-164.69

65

1950-2014

Egypt

eg

2.18***

0.64***-118.1365

1950-2014

Libya

ly

1.52

0.97***-13.2065

1950-2014

Moroccoma

1.67

0.98***-220.3665

1950-2014

Sudan

sd

1.14***

0.93***-175.2965

1950-2014

Tunisiatn

2.49***

0.90***-212.59

65

1950-2014

BIC

N

PeriodBotswanabw

2.74***

0.95***-186.65

65

1950-2014

Lesothols

2.69***

0.81***-176.8565

1950-2014

Namibiana

1.49***

0.96***-226.2765

1950-2014

South Africaza

1.46***

0.97***-290.40

65

1950-2014

Swazilandsz

1.87***

0.97***-192.6165

1950-2014

BIC

N

PeriodSouthern Africa

Western Africa

Code

Code

Elasticity（β） L..1（γ）

Elasticity（β） L..1（γ）

24

Beninbj

1.35***

0.82***-259.47

65

1950-2014

Burkina Fasobf

1.70***

0.98***-233.40

65

1950-2014

Cape Verdecv

3.13***

0.97***-171.8865

1950-2013

Cape d'Ivoireci

1.06***

0.98***-200.0965

1950-2013

Gambiagm

1.16***

0.94***-157.01

64

1950-2013

Ghana

gh

0.33

0.97***-190.7364

1950-2013

Guineagn

1.22***

0.99***-262.67

65

1950-2014

Guinea-Bissaugw

1.46**

0.97***-141.66

65

1950-2014

Liberialr

2.29***

0.99***-63.2865

1950-2014

Mali

ml

1.73***

0.89***-194.0465

1950-2014

BIC

N

PeriodWestern Africa

Code

Mauritania

mr

Niger
Nigeria

Elasticity（β） L..1（γ）
1.21***

0.91***-176.47

65

1950-2014ne

0.74**

0.94***-179.3165

1950-2014ng

1.67***

0.92***-144.9065

1950-2014

Senegalsn

1.04***

0.87***-238.8265

1950-2014

Sierra Leonesl

1.63***

0.96***-178.72

65

1950-2014

Togo

tg

1.14***

0.97***-180.9065

1950-2014

BIC

N

PeriodChina

cn

3.72**

0.99***-150.3865

1950-2014

China, Hong Kong SAR

hk

2.39***

0.99***-189.3165

1950-2014

Dem. People's Republic of Korea*kp

1.85**

0.98***-106.1459

1950-2008

Japan

jp

3.82***

0.98***-335.15144

1870-2014

Mongoliamn

2.34

0.98***-219.33

65

1950-2014

Republic of Korea

kr

0.96

0.998***-153.30104

1911-2014

BIC

N

PeriodEastern Asia

Code

Elasticity（β） L..1（γ）

Elasticity（β） L..1（γ）

Central Asia

Code

Kazakhstan

kz

4.13

0.97***-51.21

25

1990-2014

Kyrgyzstan

kg

1.28

0.94***-40.0025

1990-2014

Tajikistan

tj

0.31

0.96***-19.9025

1950-1974

Turkmenistan

tm

1.23

0.97***-29.3325

1950-1974

Uzbekistan

uz

2.27

0.94***-58.6325

1990-2014

Elasticity（β） L..1（γ）

BIC

N

Period0.91***-150.2565

1950-2014

Southern Asia

Code

Afghanistanaf

1.23***

Bangladesh

bd

1.47

0.99***-213.59

65

1950-2014

India

in

1.62***

0.996***-415.57131

1884-2014

Iran (Islamic Republic of)ir

1.68***

0.96***-144.0665

1950-2014

Nepal

np

1.85***

0.97***-268.34

65

1950-2014

Pakistanpk

1.85***

0.83***-297.59

65

1950-2014

Sri Lankalk

1.51***

0.996***-466.01

145

1870-2014

BIC

N

PeriodElasticity（β） L..1（γ）

South-Eastern Asia

Code

Brunei DarussalamBr0.80***

0.72**-112.0125

1990-2014

Cambodiakh

2.16***

0.94***-144.47

65

1950-201425

Indonesia

id2.28***

0.97***-208.1966

1949-2014

Lao People's Democratic Republicla1.88**

0.99***-273.67

65

1950-2014

Malaysia

my2.34***

0.93***-203.35

68

1947-2014

Myanmar*mm

2.34

0.98***-147.0159

1950-2008

Philippines

ph1.61***

0.98***-184.40

69

1946-2014

Singaporesg

1.27***

0.99***-185.78

65

1950-2014

Thailandth

2.82***

0.99***-219.2365

1950-2014

Viet Nam

vn

1.96*

0.99***2-191.2065

1950-2014

BIC

N

PeriodElasticity（β） L..1（γ）

Western Asia

Code

Armeniaam

0.83

0.95***-13.01

25

1950-2014

Azerbaijan

az

2.74

0.95***-13.0625

1990-2014

Bahrainbh

1.25***

0.98***-218.53

65

1950-2014

Georgiage

0.53

0.93***-6.24

25

1990-2014

Iraq

iq

1.30***

0.91***-20.4865

1950-2014

Israelil

2.18***

0.82***-218.33

65

1950-2014

Jordanjo

1.35***

0.90***-144.0265

1950-2014

Kuwaitkw

0.60***

0.88***-53.8665

1950-2014

Lebanonlb

1.38***

0.85***-128.9465

1950-2014

Oman

om

1.71***

0.98***-82.6765

1950-2014

Qatar

qa

0.75**

0.97***-106.0465

1950-2014

Saudi Arabiasa

1.53***

0.98***-170.2465

1950-2014

Syrian Arab Republicsy

1.66***

0.74***-120.79

59

1820-2009

Turkeytr

2.33***

0.85***-238.2592

1922-2014

United Arab Emirates

ae

0.81***

0.97***-142.67

65

1950-2014

Yemen

ye

1.43***

0.98***-195.2364

1950-2013

BIC

N

PeriodEastern Europe

Code

Elasticity（β） L..1（γ）

Belarusby-10.300.94***-54.8425

1990-2014

Bulgariabg

2.77

1.00***-174.0965

1950-2014

Czech Republic

cz

5.43

0.96***-26.6424

1990-2013

Hungaryhu

2.77

1.00***-198.38

69

1946-2014

Polandpl

2.92**

0.99***-216.4565

1950-2014

Republic of Moldova

md

1.40

0.94***-20.71

25

1950-2014

Romaniaro

2.56*

1.00***-182.00

65

1950-2014

Russian Federationru-15.250.96***-56.4725

1990-2014

Slovakiask

1.85

0.98***-53.9225

1990-2014

Ukraineua

0.32

0.94***-32.11

25

1990-2014

Elasticity（β） L..1（γ）

BIC

N

Period-723.89195

1820-2014

Northern Europe

Code

Denmarkdk

2.63*

Estoniaee-0.54

0.95***-41.5425

1990-2014

Finlandfi

2.00***

0.999***-467.42155

1860-2014

Irelandie

2.50***

0.999***-333.0694

1921-2014

Latvialv-0.87

0.90***-26.8525

1990-201426

0.99***

Lithuania

lt

-2.14

0.88***-38.0725

1990-2014

Norwayno2.89***

0.996***-664.86

185

1830-2014

Swedense

3.00***

0.997***-717.18

195

1820-2014

United Kingdomgb

2.21***

0.999***-747.43

185

1830-2014

Southern Europe

Code

BIC

N

PeriodElasticity（β） L..1（γ）

Albaniaal

1.80

0.99***-148.1865

1950-2014

Bosnia and Herzegovina

ba

0.24

0.95**

1.60

25

1990-2014

Croatiahr-1.42

0.88***-49.6824

1991-2014

Greecegr

3.97***

0.95***-161.61102

1913-2014

Italy

it

4.07***

0.99***-444.99

154

1861-2014

Portugalpt

2.61***

1.00***-497.57

150

1865-2014

Serbiars-7.87

0.93***-14.01

19

1990-2008

Sloveniasi

1.63**

0.96***-178.72

65

1950-2014

Spain

es

3.30***

0.98***-533.53165

1850-2014

TFYR Macedonia

mk

7.61***

0.93***-95.4525

1990-2014

Western Europe

Code

Elasticity（β） L..1（γ）

BIC

N

PeriodAustriaat

3.97*

0.99***-268.38

145

1870-2014

Belgiumbe3.23***

0.99***-601.43169

1846-2014

Francefr

5.45***

0.95***-570.21

195

1820-2014

Germanyde

4.59***

0.99***-399.19164

1850-2014

Netherlands

nl

2.23***

0.98***-530.62195

1820-2014

Switzerlandch

3.38***

0.88***-495.06165

1850-2014

Caribbean

Code

BIC

N

PeriodElasticity（β） L..1（γ）

Cuba

cu

1.72***

0.89***-152.9285

1929-2013

Dominican Republicdo

1.67***

0.88***-204.9065

1950-2014

Grenada

gd

1.33

4.50

-190.7364

1950-2013

Haiti

ht

0.40***

0.98***-384.8270

1945-2014

Jamaicajm

2.68***

5.67-209.4665

1950-2014

Puerto Ricopr

4.13***

0.97***-241.64

64

1950-2013

Trinidad and Tobagott

3.03***

0.97***4.

-187.2265

1950-2014

BIC

N

Period92
Central America

CodeElasticity（β） L..1（γ）

Costa Rica

cr

1.76***

0.88***-252.4295

1920-2014

El Salvador

sv

0.88***

0.998***-318.4495

1920-2014

Guatemalagt

1.50***

0.86***-225.2595

1920-2013

Hondurashn

0.89***

0.998***-343.5495

1920-2014

Mexicomx

1.77***

0.90***-410.27115

1900-2014

Nicaragua

ni

1.27*

0.53***-40.5630

1920-1949

Panamapa

2.01***

0.96***-222.7370

1945-2014

BIC

N

Period-313.74

109

1900-2008

South America
Argentina*

Code
ar

Elasticity（β） L..1（γ）
1.59***

27

0.90***

Bolivia (Plurinational State of)bo

1.50***

0.95***-246.57

70

1945-2014

Brazilbr

1.78***

0.98***-477.96

145

1870-2014

Chile

cl

1.95***

0.94***-505.46

195

1820-2014

Colombiaco

1.84***

0.96***-487.88115

1900-2014

Ecuadorec

1.76***

0.93***-278.7075

1939-2013

Paraguaypy

1.46***

0.96***-226.5276

1939-2014

Peru

pe

1.97***

0.98***-361.81119

1896-2014

Uruguayuy

1.54***

0.97***-323.67

145

1870-2014

Venezuela (Bolivarian Republic of)ve

1.58***

0.99***-238.74

115

1900-2014

BIC

N

PeriodNorthern America

CodeElasticity（β） L..1（γ）

Canadaca

2.16***

0.93***-434.28

145

1870-2014

United States of Americaus

2.23***

0.96***-422.39

145

1870-2014

Australia/New Zealand

Code

BIC

N

PeriodElasticity（β） L..1（γ）

Australia

au1.71***

0.98***-502.45195

1820-2014

New Zealandnz

1.55***

0.98***-432.86

144

1870-2013* p<0.05, ** p<0.01, *** p<0.001

1 In policy discourse, population decline is often taken to be synonymous to working -age population de-cline and a shortage of labor, which may be supplanted by such technology as artificial intelligence androbots. This argument focuses only on supply-side effects and fail to recognize the importance of the demand-side effects.
2
Our database can be accessed at http://www.apir.or.jp/database3
If we ran a simple OLS regression with GDP as a dependent variable and population as an independent
variable, we would obtain a very high coefficient of determination. However, the very small Durbin Watson statistics would suggest that the observed correlation is just spurious. The AR model was conceived to avoid this statistical problem.
4
We use the two-letter country code supplied by the International Standardization Organization.
5
Other OPEC economies had elasticity greater than 1.
6
The term ‘resource curse’ normally refers to the paradox that relatively resource -rich economies tend togrow more slowly than resource-poor economies. See Auty (1993) and Frankel (2010).
7
GDP data for the 12 countries that belonged to the former Soviet Union is availabl e only from 1990 in
the World Bank database. In 1991, the Soviet Union was formally dissolved into these 12 countries, oneof which was the Russian Federation. The 12 countries show a common characteristic of decreasing po pulation and increasing GDP. However, the small number of samples hinders any meaningful statisticalanalysis.
8 World Bank List of Economies (July 2016).
9
However, the world total population keeps rising toward 2100.
10
In the literature, this term usually means a modal shift in populati on growth from stagnation to acceleration, or the reverse of this. See, for example, Bloom, Canningand Sevilla (2001).
11
Actually, the IPSS’s population forecast extends to 2110.
12
No data is available for 1945. We bridged 1944 data and 1946 data for the 1 945 estimate.
13
The Japanese government simulates that 1% growth in GDP is necessary for their fiscal rebalancing
target in 2020.

28