Growth Convergence and the - Recherche en IA spécialisée au MIT

Growth Convergence and the
Middle-Income Trap
∗
TAKATOSHI ITO

Emerging market economies in East Asia have followed a similar growth path
(growth convergence) from a low-income, high-growth state to a middle-income,
middle-growth state through industrialization. The economic development of
Japan was followed by the “four tigers” (Hong Kong, Chine; the Republic of
Korea; Singapore; and Taipei,Chine) in the 1970s; and subsequently by members
of the Association of Southeast Asian Nations in the 1980s and the People’s
Republic of China in the 1990s and 2000s.

The growth rates of Asian economies are slowing over time and may fall
to advanced economy levels before incomes fully catch up with the advanced
économies. This is deﬁned as the middle-income trap in the paper.

This paper proposes that there exist three convergence paths in Asia: faible
revenu, middle income, and high income. Economies need to shift from one
convergence path to a higher one by implementing economic and political
reforms that can generate innovation. Without reform, economies may fall into
a low- or middle-income trap.

Mots clés: Asian ﬁnancial crisis, global ﬁnancial crisis, growth convergence,
middle-income trap
Codes JEL: O11, O14, O33, O40

je. Introduction

Over the past several decades, East Asian economies have achieved higher
economic growth rates than economies in other regions. These Asian economies
have all followed a similar growth path (growth convergence) from a low-income,
high-growth state to a middle-income, middle-growth state through industrialization.
Among them, Japan and Singapore have reached advanced economy status. Le
economic development of Japan was ﬁrst followed by the “four tigers” (Hong Kong,
Chine; la République de Corée; Singapore; and Taipei,Chine) in the 1970s; et
subsequently by members of the Association of Southeast Asian Nations (ASEAN)
in the 1980s and the People’s Republic of China (RPC) in the 1990s and 2000s.

Ito: Professeur, School of

∗Takatoshi
and Public Policy, Columbia University. E-mail:
ti2164@columbia.edu. This paper is based on a Distinguished Speakers Program lecture delivered at the Asian
Development Bank in Manila on 7 Janvier 2016. The author would like to thank Shang-Jin Wei, Giovanni Capannelli,
Chalongphob Sussangkarn, other participants at the lecture, and the managing editor for helpful comments. The usual
disclaimer applies.

International

Revue du développement en Asie, vol. 34, Non. 1, pp. 1–27

C(cid:3) 2017 Banque asiatique de développement
et Institut de la Banque asiatique de développement

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2 ASIAN DEVELOPMENT REVIEW

The history of economic development in Asia comprises several distinct
étapes. In the 1950s, Japan was already experiencing rapid growth of 10% annuellement.
Cependant, this was viewed as an isolated example of a prewar industrial powerhouse
in Asia returning to the level of development it enjoyed before the devastation of
the Second World War. Entre-temps, other Asian economies were still struggling
to establish effective forms of government after gaining their independence from
colonial powers.1 Most Asian economies were characterized by populous urban
areas with widespread poverty and stagnant agrarian sectors in rural areas. The most
inﬂuential work at the time, Gunnar Myrdal’s Asian Drama, offered a pessimistic
view of the region’s prospects for economic development. He argued that the burden
of large populations, among other factors, was too great to overcome.

In the 1960s and 1970s, the “four tigers”—Hong Kong, Chine; the Republic of
Korea; Singapore; and Taipei,China—experienced rapid and accelerating growth.
Both the Republic of Korea and Singapore had strong governments that pursued
industrial policy—government planning to encourage particular industries through
zoning, subsidies, and the allocation of credit. These two economies increased their
production and export of goods in sectors that Japanese industries had yielded in
order to move to higher value-added goods. The success of the four tigers eventually
prompted policy changes in Southeast Asian economies. Growth rates in Indonesia,
Malaisie, and Thailand started to rise in the mid-1980s. As rapid growth spread to
these ASEAN economies, Asia began attracting increased global attention. Dans 1993,
the World Bank painted a very positive picture of East Asian industrialization,
export-oriented policies, and equitable growth in The East Asian Miracle, lequel
replaced Asian Drama as a representative view of the region.

The positive view of East Asia suffered a brief setback in the wake of the
1997/98 Asian ﬁnancial crisis (AFC). The currency crises in East Asia—particularly
in Indonesia, la République de Corée, et la Thaïlande, all of which required International
Monetary Fund assistance—were blamed on crony capitalism and excessive risk in
the banking sector, among other factors. The image of manufacturing success was
replaced by one of ﬁnancial failure. Cependant, most Asian economies experienced
a V-shape recovery and learned valuable lessons from the experience. Banking
sectors were reformed and foreign reserves were accumulated as a buffer against
volatile capital ﬂows. During the 2008–2009 global ﬁnancial crisis (GFC), no Asian
banks failed due to collapsing values for asset-backed securities and related ﬁnancial
des produits. The damage to East Asian growth during the GFC was much shallower
than that endured during the AFC.

Cependant, growth rates in Asian economies today are slowing down to those
of advanced economy levels. A fear is that these economies will never catch up
with the income levels of advanced economies and instead will be trapped in

1Most Asian economies were colonized by a European power, except for Thailand, which was never colonized,

and the Philippines, which was colonized ﬁrst by Spain and then by the United States (NOUS).

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GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 3

middle-income status. Several factors contribute to this pessimism. Japan has
experienced 2 decades of stagnation. En même temps, the PRC has excelled on all
fronts of industry, leaving behind some of its neighboring economies that have not
been able to similarly overcome constraints to growth such as a lack of infrastructure
and human capital development.

In order to explain the long-run growth experiences of Asian economies
in a more generalized framework, growth convergence regressions are applied.
Growth theory predicts that a low-income state tends to record high growth
and that the growth rate gradually becomes lower as the income level becomes
higher. The inverse relationship between income level and the growth rate is often
depicted as a downward-sloping convergence line. This relationship is derived
from diminishing returns to capital. The convergence path has often been evident
in time series data for individual economies, but it has been difﬁcult to ﬁnd in
cross-section or panel data. Within a group of economies such as the Organisation
for Economic Co-operation and Development, a common convergence path can be
trouvé. Cependant, an attempt to ﬁnd a global cross-sectional or panel relationship
of convergence often fails. This is understandable since a global convergence
path assumes that economies’ production functions, including their technological
level and productivity, are identical and the only difference is the initial level of
capital (per capita). Donc, an unconditional convergence is refuted easily.
The literature instead favors conditional convergence that allows for differences
in culture, géographie, colonial heritage, and other socioeconomic variables as initial
conditions. Ainsi, there can be different convergence lines for different groups of
économies.

In the failed attempt to ﬁnd unconditional convergence, East Asian economies
show positive forecast errors, which means that East Asian economies recorded
higher growth rates than South Asian, African, and Latin American economies at the
same income levels. Ainsi, developing East Asian economies have moved toward
advanced economy income levels much faster than economies in other regions.
Although the “Asian Miracle” can be attributed to many factors, it remains untested
whether East Asia as a region can be treated as one group and if the experiences
across the region are common.

This paper focuses on growth convergence in East Asia. It looks at panel data
for major economies in the region. The ﬁrst test is whether they share a common,
unconditional convergence path, which appears not to be the case. Plutôt, this paper
ﬁnds three distinct convergence paths in East Asia: (je) one path that converges to
a low-income steady state, (ii) another that converges to a middle-income steady
state, et (iii) a third that converges to a high-income steady state. An economy can
shift from one convergence line to a higher one by implementing economic reforms,
such as the opening of the PRC’s economy beginning in 1978 and Viet Nam’s doi
moi (reconstruction) policy launched in 1986. Without reform, an economy may
end up in the poverty trap (steady state of the low-income convergence path) or the

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4 ASIAN DEVELOPMENT REVIEW

middle-income trap (steady state of the middle-income convergence path). Données
suggest that the PRC is moving from a middle-income convergence path to a
high-income path and that the Philippines is moving from a low-income path to
a middle-income path. Thailand seems to be headed for the middle-income trap.

According to the hypothesis of three distinct convergence paths, the fear of
being trapped in middle-income status can be understood as the policy failure to
make a leap from one convergence line to a higher one. This leap requires economic
reforms to stimulate innovation.

The rest of the paper is organized as follows. Section II reviews the growth
performances of East Asian economies from 1985 à 2015. These economies
suffered more during the AFC than during the subsequent GFC. Section III
establishes that there is a long-run slowdown in the growth rate in almost all
economies in East Asia. Cependant, the slowdown may be perfectly natural if growth
convergence is taking place. A crucial question is whether there is a common
convergence path for all Asian economies and, if not, how many such paths exist.

Section IV establishes that in Asia there are three convergence paths: faible
revenu, middle income, and high income. Economies can and do jump from one
convergence path to another by pursuing reforms and stimulating innovation. Quand
an economy fails to jump from a middle-income convergence path to a high-income
convergence path, it is said to be caught in the middle-income trap.

II. Impacts of the 1997/98 Crise financière asiatique
and the 2008–2009 Global Financial Crisis

The GFC had signiﬁcant impacts on many economies and affected most
severely the United States (NOUS) and Europe. Asian economies suffered from negative
spillovers from the advanced economies, but the negative impact on growth was
much less than in other regions. This showed the economic resilience of the Asian
region. For emerging Asia, the dip in growth rates during the GFC was much
shallower than during the AFC. The severe impacts in Asia in 1997/98 were due to
the fact that the crisis originated in some of the region’s economies. Chiffre 1 presents
time series data (1985–2015) for real gross domestic product (PIB) growth rates of
various regions as deﬁned by the International Monetary Fund. Chiffre 1 shows that
Asia has consistently grown faster than other regions except during crisis periods,
the most serious of which was the AFC.

Chiffre 2 presents time series data (1985–2015) for the growth rates of Japan
and the four tigers (Hong Kong, Chine; la République de Corée; Singapore; et
Taipei,Chine). The ﬁgure shows that the four tigers experienced larger dips in
growth during the AFC than the GFC, while Japan exhibits the opposite pattern.
En outre, the medium-term growth trends of the four tigers declined from the
pre-AFC period (1985–1996) to the intercrises period (1999–2007), and again in
the post-GFC period (2010–2015).

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GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 5

Chiffre 1. Growth Rates: Asia versus Other Regions

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GDP = gross domestic product.
Source: International Monetary Fund. World Economic Database, Octobre 2015.
https://www.imf.org/external/pubs/ft/weo/2015/02/weodata/download.aspx

Chiffre 2. Growth Rates of Japan and the “Four Tigers”

GDP = gross domestic product.
Source: International Monetary Fund. World Economic Database, Octobre 2015.
https://www.imf.org/external/pubs/ft/weo/2015/02/weodata/download.aspx

6 ASIAN DEVELOPMENT REVIEW

Chiffre 3. Growth Rates of Members of the Association of Southeast Asian Nations

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GDP = gross domestic product.
Source: International Monetary Fund. World Economic Database, Octobre 2015.
https://www.imf.org/external/pubs/ft/weo/2015/02/weodata/download.aspx

Since the PRC seems to dominate the economic statistics of emerging Asia,
a decomposition of the region is necessary. Chiffre 3 presents growth rates over the
same time period for the ﬁve original members of ASEAN, which are collectively
referred to as ASEAN-5, to show a representative group from emerging Asia.2
(Singapore appears both in Figure 2 and Figure 3.) A long-run growth slowdown
between the 1980s and 2010s is evident. Annual growth of less than 5% in the 2010s
has prompted concerns that Indonesia, Malaisie, and Thailand could fall into the
middle-income trap. While the Philippines used to be at the bottom of the ASEAN-5
growth rankings, it has been the highest-performing economy among the ASEAN-5
in the ﬁrst half of the 2010s. The Philippines’ growth rate accelerated in the post-GFC
period when other ASEAN economies, as well as advanced economies, experienced
growth slowdowns. Over the same period, the growth rate of Singapore, despite its
high per capita income, has been comparable to those of Indonesia, Malaisie, et
Thaïlande. This implies that the income gap between Singapore and these other three
economies has not yet narrowed and that they may not be on the same convergence
chemin.

Chiffre 4 shows the growth patterns of the PRC and India in the 1985–2015
period. Under Deng Xiaoping, the PRC introduced major market-oriented reforms

2ASEAN was established in August 1967 by Indonesia, Malaisie, the Philippines, Singapore, et la Thaïlande.

GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 7

Chiffre 4. Growth Rates of the People’s Republic of China and India

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GDP = gross domestic product.
Source: International Monetary Fund. World Economic Database, Octobre 2015.
https://www.imf.org/external/pubs/ft/weo/2015/02/weodata/download.aspx

dans 1978, including the privatization of many state-owned enterprises, that gradually
opened its economy to the rest of the world. Par conséquent, its growth rate accelerated
rapidly in the 1980s before experiencing a large dip in 1989/90, which coincided with
a decline in foreign direct investment (FDI) following the 1989 Tiananmen Square
protests. Reforms continued after Deng Xiaoping’s retirement in 1992. The Shanghai
Stock Exchange was reopened in 1990 after a 41-year closure and multiple foreign
exchange rates were uniﬁed in 1994. Depuis 1991 through 2001, the PRC maintained
a very high annual average growth rate of more than 10%. Only recently has the
PRC’s growth rate slowed, which is typical for any economy that has achieved 10%
annual growth for 20 years.3

India’s economic growth over the last 30 years has been consistently lower
than that of the PRC, leading to a widening of the income gap between them. Plutôt
than a convergence, there appears to be a divergence between the two economies.
Cependant, India’s growth rate has accelerated since a balance of payment crisis in
1991 prompted widespread reforms that moved the economy away from socialism.
Aujourd'hui, India continues to pursue a gradual reform process of privatization and the
removal of regulatory barriers.

3Japan also experienced an average annual growth rate that exceeded 10% during the 1950s and 1960s before

slowing in the 1970s.

8 ASIAN DEVELOPMENT REVIEW

Tableau 1. Period Average Growth Rates
(%)

Pre-AFC Intercrises Post-GFC
1985–1996 1999–2007 2010–2015
4.7
1.4
4.8
4.4
4.3
3.3
3.6
4.4
3.0
7.7
5.1
12.1
5.9
9.8
5.4

Hong Kong, Chine
Japan
Republic of Korea
Singapore
Taipei,Chine
Malaisie
Indonésie
Thaïlande
Philippines
Cambodia
Lao PDR
Myanmar
Viet Nam
RPC
India
AFC = Asian ﬁnancial crisis, GFC = global ﬁnancial crisis,
Lao PDR = Lao People’s Democratic Republic, PRC = People’s
Republic of China.
Source: Author’s compilation.

4.8
2.8
8.2
5.7
7.1
5.5
5.9
7.6
1.3
NA
2.2
NA
4.8
8.6
3.6

2.2
0.9
2.5
2.1
2.5
3.5
4.0
2.4
4.0
5.5
5.8
6.8
4.8
7.3
5.0

III. Slowdowns in Growth

Since the GFC, many advanced economies have struggled to stimulate growth
even with highly accommodative monetary policies and ﬁscal stimulus. Some
economists have argued that advanced economies have entered a new phase marked
by secular stagnation and a slower pace of technological innovation. Others regard
the slowdown as a more normal process, considering that the GFC originated in the
advanced economies. It has been commonly observed that economies in which crises
originate suffer from dysfunctional ﬁnancial markets that drag down real economic
activité. Ainsi, the post-GFC slowdown in growth is not surprising.

Emerging market economies have also suffered a growth slowdown since the
GFC. The PRC’s growth rate slowed from 10% dans 2010 to less than 7% dans 2015.
This has led to declines in global commodity prices that have affected a number of
resource-producing economies. Other Asian economies have experienced a similar
growth slowdown in the aftermath of the GFC.

Tableau 1 summarizes the average growth rates for three periods: pre-AFC
intercrises (1999–2007), and post-GFC (2010–2015). For most
(1985–1996),
emerging East Asian economies, the post-GFC period saw growth below that of the
intercrises period preceding the GFC, which also saw slower growth than during the
pre-AFC period. Typiquement, the period average growth rates, g(period), of emerging
Asian economies is as follows:

g(1985–1996) > g(1999–2007) > g(2010–2015)

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GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 9

Three notable exceptions to this stylized fact are India, the Lao People’s
Democratic Republic (Lao PDR), and the Philippines. These three economies
experienced accelerating growth rates between the pre-AFC and intercrises periods,
and again between the intercrisis and post-GFC periods. The reasons for these gains
include improved macroeconomic policy management in the Philippines ﬁnally
bearing fruit, while in the Lao PDR the increased exports of hydropower-generated
electricity to Thailand is boosting economic growth.

Many policy makers and scholars view the postcrisis slowdown and stagnation
among emerging economies as a stylized fact, while lamenting that growth rates have
not yet recovered to their pre-GFC levels. Plus récemment, policy makers in ASEAN-5
economies have expressed concern over the middle-income trap. Although their
national income remains at upper-middle levels, their potential growth rates seem to
have declined signiﬁcantly since the GFC. Entre-temps, the PRC’s industrial potential
has caught up to ASEAN-5 levels, while innovation in ASEAN-5 economies seem to
have failed in catching up with that of Japan, la République de Corée, and Singapore.
Encore, the middle-income trap is too easy an explanation for the slowdowns in
growth observed in Table 1. The lingering effects of the GFC and the subsequent
volatility in capital ﬂows are also partially to blame, which is consistent with at
least three other hypotheses for explaining declining growth rates in emerging East
Asian economies: (je) postﬁnancial crisis slowdown, (ii) global secular stagnation,
et (iii) growth convergence.

A postﬁnancial crisis slowdown is not a unique occurrence. Reinhart and
Rogoff (2009, 2014) have argued that the median length of time needed to return to
precrisis growth levels is about 6.5 années. En fait, “[5 à 6] years after the onset
of crisis, only Germany and the US (out of 12 systemic cases) have reached
their 2007–2008 peaks in real income” (Reinhart and Rogoff 2014, 50). Ce
tendency can help explain the slowdown of growth in East Asian economies between
the pre-AFC period and the intercrises period. Cependant, it may not explain the
slowdown between the intercrises period and the post-GFC period since Asia did
not suffer a ﬁnancial crisis during the GFC. Plutôt, the slowdown experienced
during the GFC was transmitted through trade channels from advanced economies to
Asia.

Another possibility for the Asian growth slowdown is that it is in line
with global secular stagnation. Not only growth rates, but also inﬂation and real
interest rates have been declining since the early 1990s (Bean et al. 2015). Asia
may be suffering from a global lack of aggregate demand and a savings glut.
Any explanations that are consistent with secular stagnation are most applicable to
advanced economies. Ainsi, emerging Asian economies are unlikely experiencing
a state of secular stagnation; c'est, one in which persistent aggregate demand is
less than aggregate supply.

The last explanation for the growth slowdown in emerging Asia is the
theory of growth convergence. The stylized fact of slowing growth rates can be

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10 ASIAN DEVELOPMENT REVIEW

viewed as part of the process of convergence in addition to the lingering effects of
a crisis.

IV. Growth Convergence

UN.

Concept of Growth Convergence

In the growth literature,

the phenomenon known as convergence is
theoretically predicted and empirically observed. Given common technology, le
higher an economy’s income level, the slower its growth rate will become. Put
differently, a low-income economy can grow faster than a high-income economy
since the marginal contribution to the growth of capital accumulation is much higher
among low-income economies. As the Appendix details, the typical convergence
equation can be written as

g j (t) = a + b{log y j (t) − log y∗

j (t)}

where gj denotes the per capita income growth rate, a is the steady-state growth
rate, yj(t) is the country j’s per capita income, and y∗
j (t) is the output at the steady
state where the effective capital–labor ratio stays constant. The growth convergence
implies b<0. The growth rate can be decomposed into the steady-state growth rate, a, and the catch-up factor, which is the second term. The more the current per capita income level is below the steady-state level, the higher the growth rate becomes. This is what allows economy j to converge to the steady state. The steady-state income level is changing over time, since even at the steady state the growth rate is positive. Once per capita income reaches the steady state, y∗, then the second term becomes zero and per capita income increases at the constant rate of a. The steady state for economy j may not be known in reality, unless the economy reaches that stage of constant growth. However, among the advanced economies, it is expected that the steady state (or the goal of the catch-up process) is the income level and growth rate in the US. Advanced economies should converge to the US (or Organisation for Economic Co-operation and Development) level of income. If this holds true, we can substitute the US income level at time t, yU S(t), for y∗ j (t): g j (t) = a + b{log y j (t) − log yus(t)} This is the basic regression equation of growth convergence. The growth convergence predicts b < 0. In empirical research, the convergence hypothesis can be shown as the negative correlation between the period average of the per capita GDP growth rate and per capita GDP at the beginning of the period. As stated l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 11 above, low-income economies can grow faster than high-income economies. There may be several reasons for this. First, the high marginal productivity of capital in low-income economies implies a higher growth rate. This is possible even if the production function has the same speciﬁcation. Second, it is more likely that a low-income economy has a lower level of technology, which depresses the income level. However, it is possible to achieve a higher growth rate through technology transfers and learning-by-doing. For a low-income economy, imitation, not innovation, may be enough to increase total factor productivity. Third, starting from low levels of infrastructure and human capital, public spending on these public goods and education can easily increase productivity. In the conditional convergence literature, conditions are often ﬁxed at the initial point (the year in which the analysis starts) so that growth can be tracked in subsequent decades. Of course, not all low-income economies can achieve high rates of growth. There are many economies that are stuck in a low-income, low-growth state. Many factors can explain the poverty trap. For example, much of the population may be living at a minimum subsistence level so that they have to spend all of their time farming, ﬁshing, or hunting rather than increasing human capital (e.g., education) or improving productivity (e.g., machines). Hence, poverty begets poverty. Under these conditions, a large population was once considered to be a disadvantage (Myrdal 1968). Having exportable resources helps in theory, but often public sector corruption has led to the skimming of export revenues for personal beneﬁts. Many East Asian economies, which typically lack signiﬁcant natural resources, have successfully escaped the poverty trap. Scholars and policy makers in East Asian economies tend to credit industrial policies for the takeoff. Under such policies, the government directs resources and credit to industries with the best chances to become competitive in global markets. Private sector companies compete in productivity and those who succeed in exports are rewarded by the government with more resources and ﬁnancial incentives. The typical East Asian government has also spent substantial amounts on physical infrastructure networks (e.g., roads, electricity, rail, and ports) and the nationwide education system. The positive view of market-friendly interventions by benevolent governments is still prevalent in East Asia. The Asian Miracle, as portrayed by the World Bank (1993), is applicable to the experiences of Japan, the four tigers, and ASEAN-5. The typical growth convergence pattern is depicted in Figure 5. Once a takeoff from the poverty trap has occurred, often resulting from a big push by the government or signiﬁcant policy reforms, the economy reaches the growth convergence line and enjoys a virtuous circle of higher growth and more investment as the income level of the population increases. Although this view is strongly supported by time series data for economies in East Asia, any casual test or rigorous extension to other regions—such as South Asia, Latin America, and Africa—tends to fail. Cross-section and panel data analyses involving all economies in the world for which data are available fail to produce l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 12 ASIAN DEVELOPMENT REVIEW Figure 5. Growth Convergence Source: Author’s illustration. a downward-sloping convergence line (see, for example, Barro 1991). Hence, East Asia is considered the exception rather than a standard role model. A single convergence line used in an attempt to explain many economies needs a strong assumption that the speciﬁcation of the production function is identical across economies and that the only difference is the degree of capital accumulation. In reality, the technological level, whether it is embodied in labor or capital, may be vastly different across economies. Technological progress, often measured through total factor productivity, also differs, as well as the respective shares of capital and labor. Many factors that are relevant to the production function in each economy can explain differences in growth. The list ranges from historical and geographic conditions to institutions and accumulated human capital. Historical conditions can also include human capital (Barro 1991; Mankiw, Romer, and Weil 1992) and an economy’s “colonial origin” (Acemoglu, Johnson, and Robinson 2001, 2002). Demography also matters since the population’s age composition, in addition to its overall size, is important for labor inputs (Bloom, Canning, and Malaney 2000). Thus, it becomes standard to consider “conditional convergence,” in which the rate of convergence differs among different economies. Hence, convergence paths may not be unique, but rather multiple paths might exist. Theoretically, this reﬂects differences in the level of technology and its growth contribution (see, for example, Han and Wei 2015). FDI has played an important role in East Asia’s development, with the conspicuous exceptions of Japan and the Republic of Korea. FDI brings in both l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 13 physical capital and technology associated with the use of capital. Borensztein, De Gregorio, and Lee (1998) showed that FDI contributes more to growth than domestic investment, presumably due to technology transfers; but this only holds when the host economy has sufﬁcient absorptive capacity through accumulated human capital. This appears to be the case in East Asia where educational attainment is relatively high. B. Stylized Facts of Growth Convergence in Asia In the rest of this section, I will present the growth convergence pattern in East Asia and propose a framework that encompasses notions of the poverty trap, the middle-income trap, and conditional convergence.4 Three periods—pre-AFC (1985–1996), intercrises (1999–2007), and post-GFC (2010–2015)—are used as in previous sections. The crisis years (1997–1998 and 2008–2009) are omitted to avoid having average growth rates altered by these two unusual crises. The following discussion uses the period average per capita growth rates as the vertical axis and the log of per capita income (US dollars converted at market exchange rates) of the ﬁrst year of each period as the horizontal axis. The sample economies are Japan, the four tigers, the ASEAN-5, the four low-income members of ASEAN, the PRC, and India.5 Recall that the period average growth rates are shown in Table 1. For the growth convergence ﬁgures, the growth rate is taken as a vertical axis, and the income level is taken as a horizontal axis. The convergence hypothesis implies that plots of different periods of a particular economy move along the line from the northwest to the southeast. If several economies can be plotted on the same line, then those economies are expected to converge in the same growth model (technology) toward a high-income, low-growth steady state, which is the goal of development. As a ﬁrst attempt, Figure 6 includes all of the aforementioned East Asian economies and India in one graph. The connected dots for each economy are mostly downward sloping, suggesting that growth convergence is evident in the time series data of each economy. Some low-income economies show an upward-sloping line. These upward movements, which depict an acceleration of growth as the income level rises, may actually be part of the takeoff from a poverty trap that resulted from a previously dysfunctional government implementing major reforms. However, Figure 6 is not appropriate when the global leader, the US, is also moving toward the right on the convergence graph. To be precise, growth convergence should be interpreted as a convergence to the US income level and its steady-state growth rate of about 2% per year. 4The term middle-income trap was ﬁrst proposed by Gill and Kharas (2007). 5The four low-income ASEAN member economies are Cambodia, the Lao PDR, Myanmar, and Viet Nam. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 14 ASIAN DEVELOPMENT REVIEW Figure 6. Growth Convergence in East Asia l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GDP = gross domestic product, Lao PDR = Lao People’s Democratic Republic, PRC = People’s Republic of China. Source: Author’s calculations. In order to take this into account, the horizontal axis of Figure 7 is modiﬁed to be the log difference of an economy’s per capita income level to the log of the US per capita income level. The zero in the horizontal axis implies reaching the US per capita income level. Figure 7 shows relative convergence to the US, using the log difference to the US for the horizontal axis. It shows the general tendency of growth convergence for each economy. However, as Figure 7 includes panel data, no single convergence path can be drawn. C. Multiple Convergence Paths Figure 7 shows that three distinct groups of economies can be grouped together to share a common convergence path. Group 1 is the high-income group comprising Japan and the four tigers. Group 2 is the middle-income group comprising the PRC, Indonesia, Malaysia, Thailand, and the post-GFC Philippines. Group 3 is the low-income group comprising Cambodia, the Lao PDR, Myanmar, and Viet Nam, as well as India and the pre-AFC and intercrises Philippines. GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 15 Figure 7. Growth Convergence in East Asia: Relative to the US l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GDP = gross domestic product, Lao PDR = Lao People’s Democratic Republic, PRC = People’s Republic of China, US = United States. Source: Author’s calculations. Japan and the four tigers clearly belong to the same group as the plots for each of these economies line up on a straight convergence line with little deviation. The PRC seems to have moved from the low-income group to the middle-income group and is approaching the high-income group. Both Indonesia and the Philippines are on the border area between Groups 2 and 3, while exhibiting atypical time series behavior in that they are not downward sloping. Indonesia has a lower growth rate and per capita income level during the intercrises period than in either the pre-AFC or post-GFC periods, reﬂecting lasting damage from the AFC that included a signiﬁcant income decline and the depreciation of the rupiah. Intercrises Indonesia is close to being in the low-income group, while during the pre-AFC and post-GFC periods, it is closer to being in the middle-income group. The Philippines’ time series data show upward movement; its growth accelerated as the income level rose, which is the opposite of what growth convergence predicts. This unusual behavior may be due to long-term improvements in socioeconomic and political conditions over a 30-year period. Political stability and better governance after the AFC and, in particular, after the GFC are often credited with improving the investment climate in the Philippines. 16 ASIAN DEVELOPMENT REVIEW I will now examine the following cases: Case 1. Indonesia is in the middle-income group and the Philippines is in the low-income group. Case 2. Both Indonesia and the Philippines are in the low-income group. Case 3. Indonesia in the intercrises period is in the low-income group and in the other two periods is in the middle-income group. The Philippines in the pre-AFC and the intercrises periods is in the low-income group and in the post-AFC period is in the middle-income group. For each case, regression analysis is conducted to ﬁnd the convergence line with the following speciﬁcation which is consistent with g j (t) = a + b{log y j (t) − log yus(t)} where t = 1 (pre-AFC), 2 (intercrises), or 3 (post-GFC); j denotes economy j; and b < 0 is expected. The cross-section, time series pooled regression is conducted. Then the growth convergence line for each group of economies is found through estimates of a and b. Table 2 shows the regression results for all three Indonesia–Philippines cases mentioned above. Using the estimated values of a and b, growth convergence lines can be superimposed on Figure 7. Figure 8 shows the ﬁtted lines of the regressions for Case 1. The convergence line for Group 1 seems to have only small deviations (errors). However, both Groups 2 and 3 have wide variations around them. Similarly, Figures 9 and 10 show the growth convergence lines for Cases 2 and 3, respectively, since it is an open question as to whether or not Indonesia and the Philippines should be included in the middle-income group. With all three cases presented, it serves as a robustness test regarding the grouping of economies. All three ﬁgures show downward-sloping convergence lines. Convergence lines are almost parallel in Case 3. In all cases, the middle-income convergence reaches the steady-state growth rate, g, of 2%, but does not reach the level of the high-income steady state. Hence, it is not a matter of fast or slow convergence with the high-income steady state, but the middle-income trap does exist. To avoid it, economies on the middle-income convergence line have to eventually make the jump to the high-income convergence line. The three convergence lines suggest that if an economy fails to jump from one convergence path to a higher one, then the economy will end up in a state in which the gap with the US income level cannot be narrowed. D. Conditional Convergence with Jumps Figure 11 explains in a schematic way how jumps are required to avoid a trap: one type of jump is from a low-income convergence path to a middle-income one, l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 17 ; a e r o K f o c i l b u p e R ; n a p a J ; a n i h C , g n o K g n o H : 1 e s a C a n i h C , i e p i a T d n a ; e r o p a g n i S ; a e r o K f o c i l b u p e R ; n a p a J ; a n i h C , g n o K g n o H : 2 e s a C ; a e r o K f o c i l b u p e R ; n a p a J ; a n i h C , g n o K g n o H : 3 e s a C a n i h C , i e p i a T d n a ; e r o p a g n i S a n i h C , i e p i a T d n a ; e r o p a g n i S d n a l i a h T d n a , a i s y a l a M , a i s e n o d n I , C R P : 1 e s a C d n a l i a h T d n a , a i s y a l a M , a i s e n o d n I , C R P : 2 e s a C a i s e n o d n I ; d n a l i a h T d n a ; a i s y a l a M ; C R P : 3 e s a C ) 3 = t ( s e n i p p i l i h P ; ) 3 , 1 = t ( , r a m n a y M , R D P o a L , a i d n I , a i d o b m a C : 1 e s a C m a N t e i V , s e n i p p i l i h P , R D P o a L , a i s e n o d n I , a i d n I , a i d o b m a C : 2 e s a C ; R D P o a L ; ) 2 = t ( a i s e n o d n I ; a i d n I ; a i d o b m a C : 3 e s a C m a N t e i V , s e n i p p i l i h P , r a m n a y M m a N t e i V ; ) 2 , 1 = 5 0 0 . 0 1 3 0 . 0 − 2 7 1 . 6 − 0 0 0 . 0 6 1 0 . 0 5 0 0 . 0 8 9 2 . 3 6 0 0 . 0 6 2 7 . 0 5 1 β α 7 0 0 . 0 1 2 0 . 0 4 2 0 . 0 − 1 1 0 . 0 − 9 0 0 . 0 6 1 6 . 0 2 1 2 . 3 − 8 1 5 . 0 − 9 5 4 . 0 2 1 β α 8 0 0 . 0 3 3 0 . 0 5 3 0 . 0 − 9 8 0 . 0 − 9 0 3 . 4 − 1 1 7 . 2 − 1 0 0 . 0 7 1 0 . 0 t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p 5 0 0 . 0 1 3 0 . 0 − 0 0 0 . 0 2 7 1 . 6 − 6 1 0 . 0 5 0 0 . 0 8 9 2 . 3 6 0 0 . 0 6 2 7 . 0 5 1 β α 7 0 0 . 0 1 2 0 . 0 6 2 0 . 0 − 3 1 0 . 0 − 0 1 0 . 0 9 4 5 . 0 7 1 5 . 3 − 9 2 6 . 0 − 7 8 5 . 0 9 β α 7 0 0 . 0 7 2 0 . 0 4 2 0 . 0 − 2 4 0 . 0 − 7 3 5 . 3 − 4 8 5 . 1 − 3 0 0 . 0 2 3 1 . 0 9 3 . 0 9 1 t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p t n e i c ﬁ f e o C r E D T S q s r a b - R s b o # t a t s - t t a t s p 5 0 0 . 0 1 3 0 . 0 − 0 0 0 . 0 2 7 1 . 6 − 6 1 0 . 0 5 0 0 . 0 8 9 2 . 3 6 0 0 . 0 6 2 7 . 0 5 1 β α 8 0 0 . 0 9 1 0 . 0 − 0 4 0 . 0 9 5 3 . 2 − 1 0 0 . 0 3 2 0 . 0 0 5 0 . 0 1 6 9 . 0 3 9 2 . 0 2 1 β α 8 0 0 . 0 1 3 0 . 0 1 3 0 . 0 − 1 7 0 . 0 − 1 0 0 . 0 9 3 0 . 0 3 7 9 . 3 − 2 8 2 . 2 − 6 9 4 . 0 6 1 r E D T S t a t s - t t a t s p q s r a b - R s b o # t n e i c ﬁ f e o C 1 p u o r G t n e i c ﬁ f e o C 2 p u o r G r E D T S t a t s - t t a t s p q s r a b - R s b o # r E D T S t a t s - t t a t s p q s r a b - R s b o # t n e i c ﬁ f e o C 3 p u o r G t ( s e n i p p i l i h P ; r a m n a y M l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . 9 3 5 . 0 6 1 / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 . a n i h C f o c i l b u p e R s ’ e l p o e P = C R P , c i l b u p e R c i t a r c o m e D s ’ e l p o e P o a L = R D P o a L . s n o i t a l u c l a c s ’ r o h t u A : e c r u o S e c n e g r e v n o C l a n o i t i d n o C . 2 e l b a T β α 3 e s a C β α 2 e s a C β α 1 e s a C 18 ASIAN DEVELOPMENT REVIEW Figure 8. Three Groupings of Economies—Case 1 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GDP = gross domestic product, Lao PDR = Lao People’s Democratic Republic, PRC = People’s Republic of China, US = United States. Source: Author’s calculations. and the other jump is from a middle-income convergence path to a higher-income one. A group of economies belongs to the same convergence line. For example, Japan and the four tigers belong to one convergence line, while middle-income ASEAN economies share another line. The low-income ASEAN economies also have a common convergence path. This means that economies that belong to the same convergence path have a similar level of technology. The difference among them is the degree of capital accumulation. The PRC maintains a relatively high growth rate although its per capita income level is approaching the top of the middle-income range. Although the PRC’s growth rate is declining slightly, it still seems possible for it to avoid the middle-income trap. E. Middle-Income Trap in the Context of Growth Convergence Within the framework proposed above, the middle-income trap is understood as a result of failing to make the jump from the middle-income convergence path to GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 19 Figure 9. Three Groupings of Economies—Case 2 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GDP = gross domestic product, Lao PDR = Lao People’s Democratic Republic, PRC = People’s Republic of China, US = United States. Source: Author’s calculations. the high-income convergence path. Hence, growth convergence results in a steady state that is lower than the steady state of the advanced economies (or the US). When an economy’s growth rate is equal to the long-run per capita growth rate of the US, the gap with the US in terms of per capita income (position on the horizontal axis) stays constant. When an economy follows the middle-income convergence path to the steady state, the income gap remains permanently and the economy is said to be stuck in the middle-income trap. In fact, it is not a trap, but rather a failure to adopt innovation and progress in the use of technology. For example, while Thailand is approaching an average per capita growth rate of 2%, it may fail to catch up to the per capita income level of the US unless it makes a shift toward innovation. Aiyar et al. (2013) conducted an investigation very similar to this study in which they compared time series data for Asian and Latin American emerging market economies and deﬁned the middle-income trap as a sudden deceleration in growth. By using probit regressions, they argue that “(i) middle-income economies are, in fact, disproportionately likely to experience growth slowdowns, and (ii) this 20 ASIAN DEVELOPMENT REVIEW Figure 10. Three Groupings of Economies—Case 3 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GDP = gross domestic product, Lao PDR = Lao People’s Democratic Republic, PRC = People’s Republic of China, US = United States. Source: Author’s calculations. Figure 11. Punctuated Conditional OECD = Organisation for Economic Co-operation and Development. Source: Author’s illustration. GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 21 result is robust to a wide range of income thresholds for deﬁning ‘middle income’ ” (Aiyar et al. 2013, 12). Then, they go on to examine factors that cause sudden growth slowdowns. The difference between my approach and that of Aiyar et al. (2013) is the assumption here that multiple growth convergence lines exist so that the middle-income steady state can be arrived at through a gradual slowdown, which is in contrast to the idea that a middle-income economy can fall off from the growth convergence line. Felipe, Kumar, and Galope (2014) also examined economies’ transitions across income groups. They searched for evidence that supports the existence of the middle-income trap; that is, an economy that is stuck in middle-income status. They refuted this proposition in favor of a hypothesis that there can be a slow, rather than a fast, transition from middle- to high-income status. Im and Rosenblatt (2013) examined transition phases in the cross-economy distribution of income. Their transition matrix analysis provides little support for the idea of a middle-income trap. Han and Wei (2015) also conducted transition matrix analysis and rejected the existence of an unconditional middle-income trap. They argued that there are factors—such as working-age population, ﬁnancial development, and macroeconomic stability—that differentiate fast- and slow-growing economies. Eichengreen, Park, and Shin (2012, 2013) argued that there are certain income levels at which a sudden slowdown tends to occur: $10,000–$11,000 and $15,000–$16,000 (in 2005 dollars and in purchasing power parity terms). It is not clear whether they argue that this slowdown is a natural process of middle-income growth convergence or the result of falling off from the high-income growth convergence path. However, their conclusion is that “slowdowns are less likely in countries where the population has a relatively high level of secondary and tertiary education and where high-technology products account for a relatively large share of exports” (Eichengreen, Park, and Shin 2013; i). Meanwhile, this paper’s ﬁnding is that an economy needs innovation to jump from the middle-income convergence path to a high-income convergence path. Bulman, Eden, and Nguyen (2014) argue that the determinants of growth at low-income levels are different from those at high-income levels. Their model implies that the transition from low- to high-income status can be smooth if an economy redirects its resources to factors that are important for high-income growth. The implication is that a middle-income trap does not exist. Robertson and Ye (2013), in contrast to the above papers, conﬁrmed the existence of a middle-income trap, which is the state in which an economy’s per capita income will not rise beyond the middle-income range over an inﬁnite period of time into the future. They tested their hypothesis with the Augmented Dickey–Fuller unit root test, which was not immediately conclusive because this test requires a large sample and the sample size for growth convergence and the middle-income trap is limited. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 22 ASIAN DEVELOPMENT REVIEW V. Concluding Remarks This paper has taken a novel approach by deﬁning the middle-income trap in the context of growth convergence. An empirical investigation using panel data was also an innovation. However, the results are more in the form of suggestive evidence rather than hypothesis testing due to the limited sample size. With the proper grouping of economies, the estimations in this paper show that each of the selected Asian economies is following one of the three convergence paths. The ﬁndings suggest that the middle-income trap can be viewed as a middle-income economy that fails to make a jump and converge toward a high-income steady state. Furthermore, making this jump requires signiﬁcant reforms and/or a policy shift to stimulate enough innovation needed for technological progress. Admittedly, the empirical results are subject to further examination. In addition, extending the analysis to other regions is left for future research. References∗ Acemoglu, Daron. 2009. Introduction to Modern Economic Growth. Princeton: Princeton University Press. Acemoglu, Daron, Simon Johnson, and James A. Robinson. 2001. “The Colonial Origins of Comparative Development: An Empirical Investigation.” American Economic Review 91 (5): 1369–401. _____. 2002. “Reversal of Fortune: Geography and Development in the Making of the Modern World Income Distribution.” Quarterly Journal of Economics 117 (4): 1231–94. Aiyar, Shekhar, Romain Duval, Damien Puy, Yiqun Wu, and Longmei Zhang. 2013. “Growth Slowdowns and the Middle-Income Trap.” IMF Working Paper WP13/71. Barro, Robert. 1991. “Economic Growth in a Cross-Section of Countries.” Quarterly Journal of Economics 106 (2): 407–43. Bean, Charles, Christian Broda, Takatoshi Ito, and Randall Kroszner. 2015. “Low for Long? Causes and Consequences of Persistently Low Interest Rates.” Geneva Reports on the World Economy, Volume 17. Geneva: International Center for Monetary and Banking Studies. Bloom, David, David Canning, and Pia M. Malaney. 2000. “Demographic Change and Economic Growth in Asia.” Population and Development Review 26 (Supplement): 257–90. Borensztein, Eduardo, Jose De Gregorio, and Jong-Wha Lee. 1998. “How Does Foreign Investment Affect Growth?” Journal of International Economics 45 (1): 115–72. Bulman, David, Maya Eden, and Ha Nguyen. 2014. “Transitioning from Low-Income Growth to High-Income Growth: Is There a Middle Income Trap?” World Bank Policy Research Working Paper 7104. Eichengreen, Barry, Donghyun Park, and Kwanho Shin. 2012. “When Fast Growing Economies Slow Down: International Evidence and Implications for China.” Asian Economic Papers 11. ∗ADB recognizes “China” as the People’s Republic of China. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 23 _____. 2013. “Growth Slowdowns Redux: New Evidence on the Middle-Income Trap.” NBER Working Paper No. 18673. Felipe, Jesus, Utsav Kumar, and Reynold Galope. 2014. “Middle-Income Transitions: Trap or Myth?” ADB Economics Working Paper Series No. 421. Gill, Indermit S., and Himi Kharas. 2007. An East Asian Renaissance: Ideas for Economic Growth. Washington, DC: World Bank. Han, Xuehui, and Shang-Jin Wei. 2015, “Re-Examining the Middle Income Trap Hypothesis: What to Reject and What to Revive?” ADB Economics Working Paper Series No. 436. Mankiw, Gregory, David Romer, and David Weil. 1992. “A Contribution to the Empirics of Growth.” Quarterly Journal of Economics 107 (2): 407–37. Im, Fernando Gabriel, and David Rosenblatt. 2013. “Middle-Income Traps: A Conceptual and Empirical Survey.” World Bank Policy Research Working Paper No. 6594. Myrdal, Gunnar. 1968. Asian Drama: An Inquiry into the Poverty of Nations. New York: Penguin. Reinhart, Carmen M., and Kenneth S. Rogoff. 2009. This Time is Different: Eight Centuries of Financial Folly. Princeton: Princeton University Press. _____. 2014. “Recovery from Financial Crises: Evidence from 100 Episodes.” American Economic Review 104 (5): 50–55. Robertson, Peter E., and Longfeng Ye. 2013. “On the Existence of a Middle Income Trap.” University of Western Australia Economics Discussion Paper No. 13/12. World Bank. 1993. The East Asian Miracle: Economic Growth and Public Policy. Oxford: Oxford University Press. Appendix. Growth Convergence The following derivation of the convergence regression is taken from chapters 2 and 3 of Acemoglu (2009) with a few modiﬁcations and an additional complexity with heterogeneous economies. Consider a labor-augmenting, slow-growth model with a constant savings rate, s, and a constant depreciation rate, z: Y (t) = F (K (t), A(t)L(t)) (1) where Y is output, F is a production function of homogeneous of degree one, K is capital, A is the technology level, and L is labor. The effective capital–worker ratio and effective output–labor ratio are deﬁned as k(t) = K (t) A(t)L(t) With homogeneous of degree one, equation (1) can be transformed as Y (t) A(t)L(t) = F (cid:2) (cid:3) , 1 K (t) A(t)L(t) = f (k(t)) (2) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 24 ASIAN DEVELOPMENT REVIEW Per capita income is deﬁned as y(t) = Y (t) L(t) Then, using this deﬁnition of y(t) and (2) becomes y(t) = A(t) f (k(t)) (3) A change in K(t), dK(t), is a new accumulation of capital by investment, which is assumed to be equal to savings minus depreciation. d K (t) = sY (t) − z K (t) where d is the notation of time derivative (assuming a continuous time model). The growth rate of k can be deﬁned as dk k = d K K − d A A − d L L (4) where time notation (t) is omitted. Assuming a constant rate of technological progress, a, and a constant rate of labor growth, n, results in dk k = d K K − a − n Combining (4) and (5) results in dk k = sY (t) − z K (t) K (t) − a − n = sY (t) K (t) − (z + a + n) Substituting Y(t) = A(t)L(t)f(k(t)), which can be rearranged from (2), results in dk(t) k(t) = s f (k(t)) k(t) − (z + a + n) or equivalently, dk(t) = s f (k(t)) − (z + a + n) k(t) (5) (6) (7) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 25 Figure A.1. Deﬁnition of the Steady State Source: Author’s illustration. When the production function F satisﬁes certain conditions (Assumptions 1 and 2 in Acemoglu 2009), there exists a unique, globally stable steady state k∗ > 0, où

k∗ is k such that s f (k∗) − (z + un + n) k∗ = 0

The steady-state per capita income is denoted as y∗ and y∗(t) = A(t)F(k∗).

At the steady state, Y/L and K/L increases at the rate of a, which is the rate of
technological progress. Finalement, the economy will converge to a state where the
growth rate equals the technological progress rate. It is easy to show in comparative
static exercises that k∗ is an increasing function of s and A(0); c'est, the initial level
of technology and decreasing function of n and z. Figure A.1 depicts how to ﬁnd k∗
from equation (7) and a given set of parameters.

Recalling equation (3) and differentiating with respect to time, the growth

rate, g, of per capita income can be shown as

g = dy(t)
oui(t)
= d A(t)
UN(t)
(cid:2)

= a +

+ F (cid:4) (k(t)) dk(t)
F (k(t))
(cid:3) (cid:2)

F (cid:4) (k(t)) k(t)
F (k(t))

dk(t)
k(t)

(cid:3)

= a + ε (k)

dk(t)
k(t)

(8)

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w
n
o
un
d
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d

F
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m
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.

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d
toi
un
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/
un
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d

F
/

3
4
1
1
1
6
4
2
8
1
1
un
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_
un
_
0
0
0
7
9
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d

b
oui
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0
7
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2
0
2
3

26 ASIAN DEVELOPMENT REVIEW

Figure A.2. Shift in the Convergence Path

Source: Authors’ illustration.

where ε(k) ≡ f (cid:4)(k(t)) k(t)/F(k(t)) is the elasticity of the production function. Note that
0 < ε(k) < 1 and {dk(t)/k(t)} was shown in equation (6). Acemoglu (2009, 80–81) describes the process of taking the ﬁrst-order Taylor expansion of equation (6) with respect to log k(t) and substituting it into equation (8). Then, it becomes the following convergence equation (Acemoglu 2009, 81): g = dy(t) y(t) g = dy(t) y(t) ≈ a − ε (k∗) (1 − ε (k∗)) (z + a + n) (log k(t) − log k∗) ≈ a − (1 − ε (k∗)) (z + a + n) (log k(t) − log k∗) (9) The ﬁrst term is the steady-state growth rate, which is the technological progress rate. The second term is the convergence term. If y < y∗ then g > un,
and vice versa. This shows that the growth rate is a decreasing function of y,
thus the downward-sloping convergence line. This is depicted as the solid line in
Figure A.2.

The following is an application of the above summary of the theory of
convergence of Acemoglu (2009), which is needed to derive multiple convergence
lines. Suppose that at some point of time, t = t0, there was jump in technology from
UN(t0) to A+(t0), other parameters being equal, où

UN (t0) < A+ (t0) l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 GROWTH CONVERGENCE AND THE MIDDLE-INCOME TRAP 27 Then, k∗ and y∗ will become larger and the convergence line shifts to the right as depicted in the broken line in Figure A.2. As k(t) is deﬁned as K(t)/A(t)L(t), a sudden jump in the value of A will lower k(t0). However, y(t0) = A(t0) f(k(t0)) will become higher, the economy will jump from (y(t0), g(t0)) to (y+(t0), g+(t0)) to y+(t0), and the growth rate will become higher due to the convergence term. These lines correspond to the multiple convergence lines in the text. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / e d u a d e v / a r t i c e - p d l f / / / / / 3 4 1 1 1 6 4 2 8 1 1 a d e v _ a _ 0 0 0 7 9 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3
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