arXiv:1703.01292v2 [q-fin.EC] 13 Nov 2017Quantifying China’s Regional Economic Complexity Jian Gaoa,b,∗, Tao Zhoua,b,∗∗ aCompleX Lab, Web Sciences… [605788]

arXiv:1703.01292v2 [q-fin.EC] 13 Nov 2017Quantifying China’s Regional Economic Complexity
Jian Gaoa,b,∗, Tao Zhoua,b,∗∗
aCompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People’s R epublic of China
bBig Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
Abstract
China has experienced an outstanding economic expansion du ring the past decades, however, literature on non-
monetary metrics that reveal the status of China’s regional economic development are still lacking. In this paper, we
fill this gap by quantifying the economic complexity of China ’s provinces through analyzing 25 years’ firm data. First,
we estimate the regional economic complexity index (ECI), a nd show that the overall time evolution of provinces’
ECI is relatively stable and slow. Then, after linking ECI to the economic development and the income inequality, we
find that the explanatory power of ECI is positive for the form er but negative for the latter. Next, we compare di fferent
measures of economic diversity and explore their relations hips with monetary macroeconomic indicators. Results
show that the ECI index and the non-linear iteration based Fi tness index are comparative, and they both have stronger
explanatory power than other benchmark measures. Further m ultivariate regressions suggest the robustness of our
results after controlling other socioeconomic factors. Ou r work moves forward a step towards better understanding
China’s regional economic development and non-monetary ma croeconomic indicators.
Keywords: Economic complexity, Non-linear science, Economic develo pment, Network science, Entropy
1. Introduction
Understanding how economies develop to prosperity and figur ing out the best indicators that reveal the status
of economic development are long-standing challenges in ec onomics [1, 2], which have far-reaching implications
to practical applications. Traditional macro-economic in dicators, like Gross Domestic Product (GDP), are widely
applied to reveal the status of economic development, howev er, calculating these economic census-based indicators
are usually costly, resources consuming and following a lon g time delay [3]. Thanks to the data revolution of the past
decades [4], a branch of economic research has been moving to data-driven approaches within the methodology of
natural science, statistical physics and complexity scien ces [5, 6, 7], which makes it possible to introduce new metric s
that surpass the traditional economic measures in revealin g current economic status and predicting future economic
growth, with applications to economic development [8, 9], t rading behavior [10], poverty [11, 12], inequality [13, 14] ,
unemployment [15, 16], and industrial structure [9, 17]. Ec onomists and physicists have also introduced a variety
of non-monetary metrics to quantitatively assess the count ry’s economic diversity and competitiveness by measuring
intangible assets of the economic system [18, 19], allowing for quantifying the economies’ hidden potential for future
development [20, 21] in near real-time and at low cost.
In recent decades, many works on quantifying the complexity of socioeconomic systems and financial markets
have been done by physicists, who have helped to move researc h in economy forward by introducing physics-related
approaches and models into economic and financial studies [2 2, 23]. In particular, as an interdisciplinary field, the
econophysics [24, 25] applies theories and methods that ori ginally developed by physicists to solve problems in eco-
nomics and statistical finance [26]. Recently, econophysic ists have proposed network measures to reveal the true
risks associated with institutions to make financial market s more stable [27] and studied the complex correlations
and trend switchings in financial time series [28]. Moreover , economists and physicists have applied network and
∗E-mail addresses : gaojian08@hotmail.com (J. Gao)
∗∗E-mail addresses : zhutou@ustc.edu (T. Zhou)
Preprint submitted to arXiv November 15, 2017

statistical methods to reshape the understanding of intern ational trade that the knowledge about exporting to a desti-
nation diffuses among related products and geographic neighbors [29]. Besides, some physical processes like iterative
refinement and resource-allocation have been widely applie d to evaluate online reputation in socioeconomic systems
[30, 31] and to build better recommender systems in e-commer ce [32, 33]. More recent works on econophysics and
complexity are summarized by review papers [34, 35, 36] and b ooks [37, 38].
Towards quantifying the complexity of a country’s economy, the pioneering attempt was made by Hidalgo and
Hausmann [18], who modeled the international trade flows as “ Country-Product” networks and derived the Economic
Complexity Index (ECI) by characterizing the network struc ture through a set of linear iterative equations, coupling
the diversity of a country (the number of products exported b y that country) and the ubiquity of a product (the number
of countries exporting that product). The intuition behind this new branch of studies is that the cross-country income
differences can be explained by di fferences in economic complexity, which is measured by the div ersity of a country’s
“capabilities” [18, 19]. Soon after, Tacchella et al. [39] d eveloped a new statistical approach which defines a country’ s
Fitness and a product’s complexity by the fixed points of a set of non-linear iterative equations [40], where the
complexity of products is bounded by the fitness of the less co mpetitive countries exporting them. Further, Cristelli et
al. [21] studied the heterogeneous dynamics of economic com plexity and found, in the fitness-income plane, strong
explanatory power of economic development in the laminar re gime and weak explanatory power in the chaotic regime.
Based on this observation, they argued that regressions are inappropriate in dealing with this heterogeneous scenario
of economic development and further proposed a selective pr edictability scheme to predict the evolution of countries.
Nevertheless, these economic complexity indicators are no t perfect, for example, ECI su ffers from criticisms on its
self-consistent, Fitness depends on the dimension of the ph ase space of the heterogeneous dynamics of economic
complexity [20, 21], and a new variant of Fitness method, cal led minimal extremal metric, can perform even better if
for a noise-free dataset [41]. Recently, Mariani et al. [42] quantitatively compared the ability of ECI and Fitness in
ranking countries and products, and further investigated a generalization of the “Fitness-Complexity” metric.
Even though there is a body of literature on inferring comple xity [43, 44] using cross-country data recording
world trade flows [45, 46], studies on China’s regional econo mic complexity using firm level data are still missing.
On the one hand, previous studies mainly focus on measuring i nternational level economic competitiveness while the
regional level complexity within a country is always ignore d. In other words, whether the economic complexity can
be successfully extended and tested across di fferent scales is still unknown. One the other hand, most of pre vious
economic complexity analysis are based on the world trade da ta [18, 39], meaning that industries without exporting
products are excluded, such as services. However, not only g oods but also services are important to measure economic
complexity as the growth in service and its sophistication c an provide an additional route for economic growth [47].
Moreover, China has experienced a great economic expansion during the past decades. However, some questions
regarding China’s development are still puzzling, for exam ple, how did China grow [48], what happened to regional
development within China [9, 49], which metric to use in meas uring regional economic complexity [42], and what
is the predictive power of complexity to regional developme nt and inequality [14, 50]. Fortunately, the development
statistical methods (for example, methodology contribute d by econophysicists) and the availability of China’s firm
level data (dataset that includes all types of industries) p rovide us a promising way to explore the regional economic
complexity within a country, and o ffers us a chance to explore how the non-monetary economic comp lexity correlates
with traditional monetary macroeconomic indicators at the regional level.
In this paper, we study China’s regional economic complexit y by analyzing publicly listed firm data from 1990
to 2015. We start by estimating the Economic Complexity Inde x (ECI) of China’s provinces based on the structure
of the “Province-Industry” network. We show that diversifie d provinces tend to have industries of less ubiquity, and
the overall time evolution of the provinces’ rankings by ECI is relatively stable and slow, with provinces located
along the coast having higher economic complexity. Then, af ter linking complexity with the economic development
and income inequality, we find that ECI is a positive and signi ficant indicator of economic development with higher
explanatory power for provinces of lower level of GDP per cap ita (GDP pc) that located in laminar regime of ECI-
ln(GDP pc) plane compared to provinces of high level of GDP pc that located in chaotic regime. Together, ECI finds a
negative and significant explanatory power for regional inc ome inequality of China. Moreover, we compare di fferent
measures of economic diversity and explore their relations hips with monetary macroeconomic indicators. Results
suggest that Fitness is comparative with ECI, and they both p erform better than Diversity and Entropy in correlating
GDP pc. Further, we show the predictive powers of ECI and Fitn ess are robust by using multivariate regressions after
controlling other socioeconomic factors. Our work contrib utes to the literature of regional economic complexity.
2

The paper is organised in the following way. Section 2 introd uces the data and the implementation of economic
diversity metrics. Section 3 presents the results of China’ s regional economic complexity and its connections with
income inequality. Finally, Section 4 provides conclusion s and discussion.
2. Data and Methods
We study the regional economic complexity by using China’s p ublicly listed firm data, which were extracted from
the RESSET Financial Research Database, provided by Beijin g Gildata RESSET Data Tech Co., Ltd. (http: //www.resset.cn).
The data set provides basic registration information and fin ancial information of publicly listed firms in two major
stock markets (Shanghai and Shenzhen) of China between 1990 and 2015, such as listing date, delisting date, regis-
tered address, and industry category. In our data set, there are in total 2690 firms with the registered addresses coverin g
31 provinces (or municipalities) in China. For the industry , all the firms belong to 70 categories, which correspond to
the industry classification issued by the China Securities R egulatory Commission (http: //www.csrc.gov.cn) in 2011.
Some macroeconomic indicators of China at the province-lev el in the period 2000-2015 are also used, including
GDP pc, relative income, income inequality, population, ur banization, schooling, innovation and trade. The GDP pc in
the national currency (CNY) is used as a monetary metric in me asuring the level of economic development. Together,
we also use the relative income in urban area (RICU) and in rur al area (RICR) with purchasing power parity (PPP)
adjustment in China’s provinces for the year 2010, which wer e original reported by Xie and Zhou [50]. For the income
inequality, we use the relative income di fferences (RICD) as an estimation, which is defined by the ratio of RICU to
RICR to measure the level of income inequality between urban and rural areas in China. For the population, we use
the resident population at year-end. For the urbanization m etric, we use the share of urban area in a province as an
estimation. For the metrics of schooling and innovation, we use the ratio of students in higher education in a province
and the number of domestic granted patents, respectively. F or the foreign trade, we use the total value of imports and
exports of destinations and catchments. All these macroeco nomic data except for income inequality were extracted
from China Statistical Yearbook, published by the National Bureau of Statistics of China (http: //www.stats.gov.cn).
The Economic Complexity Index (ECI) [18] is proposed based o n the intuition that, in our case, sophisticated
economies are of high diversity (the number of industries on e province has) and have industries with low ubiquity
(the number of provinces with that industry), because only a few provinces can diversify into sophisticated industries
[14, 19, 43]. So combining information on the diversity of a p rovince and the ubiquity of its industries will provide
a promising way to measure the sophistication of a province’ s productive structure. To calculate ECI, we first build
a “Province-Industry” network where the weight of a link is d efined as the number of firms belonging to the corre-
sponding industry type and in the corresponding province (s ee Figure 1A for an illustration). Then, we transform this
bipartite network into an adjacency matrix Mp,i, where Mp,i=1 if province phas the revealed comparative advantage
(RCA) [51] in industry i(RCA p,i≥1) and 0 otherwise [18, 52]. Here, we define the RCA as the ratio between the
observed number of firms operating in an industry in a provinc e and the expected number of firms of that industry in
that province. Formally, the RCA for province pin industry iis defined as
RCA p,i=xp,i/summationtext
i′xp,i′/slashBigg/summationtext
p′xp′,i/summationtext
i′/summationtext
p′xp′,i′, (1)
where xp,iis the number of firms in province pthat operate in industry i. Further, the diversity of a province pis
defined as the number of industries in which the province has t he comparative advantage,
Diversity=kp,0=/summationdisplay
iMp,i. (2)
The ubiquity of industry iis defined as the number of provinces with the comparative adv antage in that industry,
Ubiquity=ki,0=/summationdisplay
pMp,i. (3)
Finally, the Economic Complexity Index (ECI) of province pis defined as
ECI p=Kp−/angbracketleft/vectorK/angbracketright
std(/vectorK)=m2Kp−m/summationtext
pKp/radicalBig
m/summationtext
p(mK p−/summationtext
pKp)2, (4)
3

used
A
P1
P2
P3I1
I2
I3
I4
Province Industryi pxB
5 10 15 20 25 30 356810121416
BJTJHESXNM
LNJLHL
SHJSZJAH
FJJX
SDHA
HBHN
GDGX
HICQ
SCGZYN
XZ
SNGSQH
NX
XJ
pkUbiquity(kp,1)
Diversity(kp,0)pkPearson'sr=-0.777
p=2.8×10-7
Figure 1: Quantifying regional economic complexity. ( A) Illustration of a “Province-Industry” bipartite network . The weight of link xp,iis the
number of firms in province pthat operate in industry i. (B) The “Diversity-Ubiquity” diagram divided into four quadr ants defined by the averaging
diversity/angbracketleftkp,0/angbracketrightand ubiquity/angbracketleftkp,1/angbracketright, as shown by the vertical and horizontal lines, respectivel y. The abbreviations of province names correspond to
Table A1 in Appendix.
where mis the number of provinces, /angbracketleft·/angbracketrightandstd(·) are respectively functions of mean value and stand deviati on that
operate on the elements in vector /vectorK, and/vectorKis the eigenvector associated with the second largest eigen value of the
matrix [40]
˜Mp,p′=1
kp,0/summationdisplay
iMp,iMp′,i
ki,0. (5)
Indeed, the matrix ˜Mp,p′is defined in terms of connecting provinces who have similar i ndustries, weighted by the
inverse of the ubiquity of an industry ( ki,0) and normalized by the diversity of a province ( kp,0) [19].
The Fitness Index [39] is based on the idea that, i) a diversifi ed province gives limited information on the com-
plexity of industries, and ii) a poorly diversified province is more likely to have a specific industry of a low level
sophistication. Therefore, a non-linear iteration is need ed to bound the complexity of industries by the fitness of the
less competitive provinces having them [20, 21]. Here, the F itness of province is proportional to the number of its
industries weighted by their complexity. In turn, the compl exity of industry is inversely proportional to the number of
provinces who have this industry (similar methods were earl y proposed to deal with recommender systems [31, 53].
The coupling of the province p’s Fitness ( Fp) to the industry i’s complexity ( Qi) is summarized in the following
non-linear iterative scheme:˜F(n)
p=/summationdisplay
iMp,iQ(n−1)
i
˜Q(n)
i=1/summationtext
pMp,i1
F(n−1)
p, (6)
where ˜F(n)
pand ˜Q(n)
iare respectively normalized in each step by F(n)
p=˜F(n)
p//angbracketleft˜F(n)
p/angbracketrightandQ(n)
i=˜Q(n)
i//angbracketleft˜Q(n)
i/angbracketrightgiven the
initial condition F(0)
p=1 and Q(0)
i=1. The non-linear iterations go until the stationary state i s reached, and the final
Fitness value reflects complexity.
3. Results
In this section, we first report the China’s regional economi c complexity ECI and its time evolution. Then, we
show the heterogeneity of the levels of economic developmen t in relation to the value of the economic complexity.
Next, we provide simple comparisons among di fferent measures of economic diversity, especially ECI and Fi tness,
and show how they correlate other monetary macroeconomic in dicators. Finally, we check the robustness of the
predictive power of the economic complexity for the economi c growth by using multivariate regressions.
4

2000 2005 2010 2015ECI(2015)
-2.0
21111
YearSH
GD
BJ
FJ
TJ
JS
HI
SN
ZJ
SD
JL
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SC
LN
GX
HB
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XZ
YN
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HE
AH
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HA
GS
SX
NX
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QH 31Ranking(ECI)2.0B A
31 21 11 13121111BJ
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HE
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JS
ZJ
AHFJ
JXSD
HAHB
HNGD
GXHI
CQSC
GZ
YNXZSN
GS
QHNXXJPearson'sr=0.898
p=7.4×10-12C
Ranking(ECI2015)
Ranking(ECI2000)
Figure 2: China’s regional economic complexity and the evol ution of provinces’ rankings. ( A) Map of China’s regional Economic Complexity
Index (ECI). The color denotes the value of ECI in 2015. ( B) Time evolution of all provinces’ rankings by ECI from 2000 t o 2015. ( C) Relationship
between rankings by ECI in 2000 and 2015. The gray dash line is the diagonal line. The abbreviations of province names corr espond to Table A1
in Appendix.
3.1. Regional Economic Complexity
The Economic Complexity Index (ECI) measures the regional e conomic structure by combining province’s di-
versity and industry’s ubiquity. To check the intuition beh ind ECI that sophisticated economies are diverse and
having industries of low ubiquity, in Figure 1B we present th e relationship between a province’s diversity ( kp,0=/summationtext
iMp,i) and the averaging ubiquity of industries in which the provi nce has the comparative advantage ( kp,1=/summationtext
i(ki,0Mp,i)//summationtext
iMp,i). We find a strong and significant negative correlation betwe enkp,0andkp,1with Pearson’s
correlation r=−0.777 ( p-value=2.8×10−7), supporting the hypothesis that diversified provinces ten d to have less
ubiquitous industries.
Figure 2A presents the values of China’s regional Economic C omplexity Index (ECI) at province level in 2015. We
find that provinces located along the coast trend to have high er economic complexity, follow by provinces that located
in Southwest and Northeast of China. Figure 2B shows the time evolution of the rankings of all provinces between
2000 and 2015 by ECI. It can be seen that provinces with highes t and lowest rankings are more stable during that
period, with Shanghai (SH), Guangdong (GD) and Beijing (BJ) ranked to the top, and Qinghai (QH), Inner Mongolia
(NM) and Ningxia (NX) ranked to the bottom. For the middle ran kings, economies in some provinces become more
sophisticated such as Shandong (SD) and Fujian (FJ) while so me provinces become less complex such as Shaanxi
(SN) and Chongqing (CQ). Figure 2C compares all rankings by E CI at the starting year 2000 and the ending year
2015. Provinces with an increased ECI rankings locate above the diagonal while provinces with decreased rankings
locate under the diagonal. We find that the ECI rankings in 201 5 are highly and significantly correlated with those in
2000 with the Pearson’s correlation r=0.898 ( p-value=7.4×10−12), indicating that the overall time evolution of
ECI rankings is relatively stable and slow.
3.2. Linking Complexity to Development and Inequality
The Economic Complexity Index (ECI) is a non-monetary metri c which is able to assess the level of development
and competitiveness of provinces by measuring intangible a ssets of economic systems [18, 21, 39]. Naturally, we
should compare this metric for province intangibles with mo netary metric, as the GDP pc, which is traditionally used
5

-2 -1 0 1 2 3101112
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-2 -1 0 1 2 38910BJ TJ
HE
SXNMLN
JL
HLSH
JS
ZJ
AHFJ
JXSD
HAHB
HNGD
GXHICQ
SC
GZYNXZSN
GSQHNXXJ
BJ
TJ
HE
SXNMLN
JLHLSH
JSZJ
AHFJ
JXSD
HAHBHNGD
GXHI
CQSC
GZYNXZSN
GSQH NXXJln(GDP pc) (2015)
ECI (2015)Pearson's r= 0.667
p= 4.1×10-5
BC
ln(GDP pc)
ECISH
GD
BJ
FJ
TJ
JS
HI
SN
ZJ
SD
JL
HL
SC
LN
GX
HB
GZ
CQ
HN
XZ
YN
XJ
HE
AH
JX
HA
GS
SX
NX
NM
QHA
ln(GDP pc) (2000)
ECI (2000)Pearson'sr= 0.554
p= 1.2×10-3
Figure 3: Relationship between economic developmet and eco nomic complexity. ( A) and ( B) show the positions of provinces in plane of Economic
Complex Index (ECI) versus natural logarithm of GDP pc in 201 5 and 2000, respectively. The gray dash line is the linear fit o f dots. ( C)
Time evolution of locations of provinces in the ECI-ln(GDP p c) plane from 2000 to 2015. During this period, the better-go ing and worse-going
provinces changed their ECIs, on average, with a value 0.49 a nd−0.40, respectively. The abbreviations of province names corr espond to Table A1
in Appendix.
by economists in measuring the level of economic developmen t. For static observations, Figure 3A and 3B show
the locations of provinces in the ECI-ln(GDP pc) plane for 20 15 and 2010, respectively. We find that the economic
complexity is a positive and significant indicator of econom ic development, as suggested by the high correlation
between ECI and ln(GDP pc) with Pearson’s correlation r=0.667 ( p-value=4.1×10−5) for 2015 and r=0.554
(p-value=1.2×10−3) for 2000. Roughly speaking, provinces with larger economi c complexity enjoy a higher level
of economic development.
To further investigate how economic development depends on the complexity, we move from the static pictures
to the dynamics of provinces in the compound ECI-ln(GDP pc) p lane from 2000 to 2015. As shown in Figure 3C,
the dynamics of the provinces in this plane is, to some extent , heterogeneous but with two emergent trends. On the
left and central sides, we observe a laminar regime, where EC I is linearly and positively correlated with ln(GDP pc),
supporting that ECI is a driving force of economic growth [21 ]. Countries locating in this laminar regime enjoy a slow
but stable economic development. On the right side, we obser ve a chaotic regime, where the dynamics of provinces
are less predictable due to the larger fluctuations of ECI. Ho wever, countries locating in this chaotic regime developed
much faster and achieved a higher level of economic developm ent. For example, Shaanxi (SN) has a much higher
ECI than the other provinces with the same level of GDP pc (for example, QH, SC, JX, AH and YN) in 2000. In
the last 15 years, the GDP pc of Shaaxi (SN) increased by a fact or of 9.6, leading its ranking by GDP pc jumped
from 23 to 14. By comparison, the GDP pc of the other provinces with the same level of GDP pc only grew, on
average, by a factor of 7.3. These results suggest that, in th e case of China, ECI is a good indicator of future economic
development for the provinces with a relatively low level of GDP pc, while the predictive power is reduced for the
provinces with a high level of GDP pc. Moreover, we notice tha t during the considered period the ECIs of some
provinces remarkably increased, for example, Shanghai (SH ) from 2.01 to 2.49 and Guangdong (GD) from 0.97 to
2.26 while the ECIs of some provinces decreased remarkably, for example, Tianjin (TJ) from 1.61 to 0.99 and Jiangxi
(JX) from−0.27 to−0.81. On average, the ECIs of better-going province (with incr easing in ECI) changed 0.49, and
the ECIs of worse-going provinces (with decreasing in ECI) c hanged−0.40 from 2000 to 2015. The result suggests
that economic complexity and regional development are hete rogeneous within a country.
6

-2 -1 0 1 20.40.60.81.01.2
-2 -1 0 1 20.10.30.50.7
-2 -1 0 1 212345
BJ TJ
HE
SXNMLN
JL
HLSH
JSZJ
AHFJ
JXSD
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HBHNGDGX
HICQ
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GSQHNX
XJ
BJ
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LNJL
HLSHJS
ZJAH
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YN
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QH NX
XJPearson'sr= -0.413
p= 2.1×10-2Pearson'sr= 0.531
p= 2.1×10-3RICU (2010)
ECI (2010)BA
Pearson'sr= 0.589
p= 4.8×10-4RICR (2010)
ECI (2010)C
RICD (2010)
ECI (2010)
Figure 4: Relationship between economic complexity and inc ome inequality. ( A) and ( B) are respectively for Economic Complexity Index (ECI)
versus relative income at urban area (RICU) and at rural area (RICR) in 2010. ( C) Relationship between ECI and relative income di fferences
(RICD). As an estimation of income inequality, RICD is define d by the ratio of RICU to RICR. The gray dash line is the linear fi t of dots. The
abbreviations of province names correspond to Table A1 in Ap pendix.
The income inequality along with economic development has a lways been a central concern of economists and
policy makers in economic theory and policy [54]. With the de velopment of new perspective and economic tools,
progresses have been made on explaining income inequality t hrough new data and measures [14, 55, 56]. For exam-
ple, Hartmann et al. [14] showed that the economic complexit y can be a significant and negative indicator of income
inequality. We here explore the relationship between econo mic complexity and income inequality on regional level
within China. First, Figure 4A and 4B show how ECI correlates with the relative income at urban area (RICU) and
at rural area (RICR), respectively. We find a positive and sig nificant correlation between ECI and the relative income
at both urban area (Pearson’s correlation r=0.531 with p-value=2.1×10−3) and rural area (Pearson’s correlation
r=0.589 with p-value=4.8×10−4). Then, we use the relative income di fferences (RICD), defined by the ratio of
RICU to RICR, as an estimation of income inequality and furth er show the relationship between ECI and RICD in
Figure 4C. We find a negative and significant correlation betw een economic complexity and relative income di ffer-
ences (Pearson’s correlation r=−0.413 with p-value=2.1×10−2), which is coincided with previous findings based
on international trade data [14]. These results suggest tha t China’s economic complexity still has negative explanato ry
power of regional income inequality, although China’s grea t economic expansion has risen regional disparities signif –
icantly higher during the last a few decades [57, 58]. Once ag ain, the results suggest the development of regions in
China is not homogenous (see GDP pc in Figure 3 and income ineq uality in Figure 4 for examples), even though the
country as whole may experience remarkable increase in econ omic complexity and development. The observations
should cause us to further explore the complexity and develo pment at both national and regional levels.
3.3. Comparing Di fferent Measures of Economic Diversity
Thanks to the development of complexity sciences, a variety of metrics have been proposed to measure the di-
versity of economies regarding their productive structure s, including Economic Complexity Index (ECI) [18], Fitness
Index [39], Diversity [18] and Entropy [59]. The ECI defines a country’s complexity and a product’s ubiquity through
a set of linear iterative equations. The Fitness Index define s a self-consistent metrics for a province’s fitness and a
product’s complexity through a set of no-linear iterative e quations that assess the advantage of diversification. The
Diversity is defined by Eq. (2), i.e., the number of industrie s in which one province has the comparative advantage.
7

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Figure 5: Comparison between Economic Complexity Index (EC I) and Fitness Index. ( A) and ( B) show the mappings of the rankings of provinces
by ECI (left) into Fitness (right) in 2005 and 2015, respecti vely. ( C) The Pearson’s correlation coe fficient between ECI and Fitness as a function of
time. All the positive correlations are significant with p-value no more than 10−6. The abbreviations of province names correspond to Table A1 in
Appendix.
The Shannon Entropy measures the diversity of industries in which one province has the comparative advantage.
First, we compare the ability of ECI and Fitness on ranking th e complexity of China’s provinces. Figure 5A and
5B present how the rankings by ECI is mapped into the rankings by Fitness in 2005 and 2015, respectively. In general,
we find that ECI and Fitness agree with each other for top ranki ngs and bottom rankings, while the two methods are
distinguishable for middle rankings. For example, Hainan ( HN) and Xinjiang (XJ) are respectively ranked 19 and
22 by ECI in 2015, while the corresponding rankings are 8 and 9 by Fitness. There are also some provinces that
are overestimated by ECI compared to Fitness in 2015, such as Tianjin (TJ: 5→15), Heilongjiang (HL: 12 →19)
and Tibet (XZ: 20 →29). To provide a quantitative comparison between the ranki ngs, in Figure 5C we show the
Pearson’s correlation rbetween ECI and Fitness as a function of time. We find a positiv e and significant correlation
between the two rankings across all years with p-value no more than 10−6. The correlation is stabilized at about 0.871
since 2011, suggesting that the rankings by ECI and Fitness a re, to some extent, consistent and stable. The result is
notable since previous studies based on world trade data fou nd inconsistency of ECI and Fitness methods in ranking
countries [20, 42]. Here, our empirical results based on firm data at regional level suggest that the two methods are
comparative. Considering that there is no ground truth in ra nkings in terms of economic complexity and the two
methods have distinctive intuitions and formulations, it i s hard to identify the best methods in practices, leaving the
problem being still complicated. Indeed, the discrepancie s of these four measures of economic diversity urge on the
development of new regional economic complexity metrics.
Next, we explore the correlations among di fferent measures of economic diversity, economic developmen t and
income inequality. As shown in the first four columns of Figur e 6, all the four economic diversity metrics have positive
and significant correlations with each other. Specifically, Fitness is highly correlated with ECI (see the second column s
of Figure 6), and Diversity is highly correlated with Entrop y (see the fourth columns of Figure 6). ECI and Fitness
have higher explanatory power for GDP pc compared to Diversi ty and Entropy, as suggested by their larger correlation
coefficients, 0.665 for ECI and 0.662 for Fitness (see the fifth colu mn of Figure 6). Also, ECI and fitness are better
indicators for relative income, compared to Diversity and E ntropy (see the sixth and seventh columns of Figure 6).
Together, we find that the correlation coe fficients in RICR column are much larger than the corresponding values in
RICU column, suggesting that the relative income in rural ar ea are more explained by economic diversity metrics
than in urban area. For the income inequality, we find that all the measures of economic diversity and economic
development are negatively and significantly correlated wi th RICD (see the last column of Figure 6), meaning that
the more economic diversity and the higher level of economic development, the less income inequality. In particular,
8

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Figure 6: Correlations between di fferent economic diversity measures and economic developmen t as well as income inequality. The economic
diversity measures include Economic Complexity Index (ECI ), Fitness Index, Diversity and Shannon Entropy. The econom ic development measures
include GDP pc, relative income at urban area (RICU) and rela tive income at rural area (RICR). The income inequality is es timated by the relative
income differences (RICD), defined by the ratio of RICU to RICR. All metri cs are averaged over the period 2010-2015 to reduce noises ex cept
for RICU, RICR and RICD, which are only for 2010. The matrix di agonal shows the histograms of each variable, the upper tria ngle shows
the Pearson’s correlation coe fficients between the pair of variables, and the lower triangle shows the corresponding scatter-plots with solid lines
representing linear fits. The correlation coe fficients are with significant level * p<0.1, ** p<0.05, and *** p<0.01.
RICR has the highest explanatory power for RICD, followed by GDP pc and RICU, suggesting that the relative
income in rural area has the potential to be the best negative indicator for income inequality in provinces. The
reason why economic complexity measures are less competiti ve than, for example, RICR, in correlating with RICD
is still puzzling, which urges for further exploration. Mor eover, we notice that ECI and Fitness are comparable with
each other in explaining economic development and income in equality as indicated by their very close correlation
coefficients (see the first two rows of Figure 6).
3.4. Robustness Check of Complexity’s Predictive Power
Using bivariate statistics in the above two sections, we hav e shown the correlations between economic diversity
measures and the level of economic development. In this sect ion, based on multivariate regressions, we further
explore whether changes in a province’s economic diversity are associated with changes in the level of economic
development after controlling the e ffects of other socioeconomic factors like Population, Urban ization, Schooling,
Innovation and Trade. If the economic diversity is a good and robust indicator for economic development, we should
observe a positive and significant correlation between the f ormer non-monetary metrics (ECI and Fitness) and the
later monetary metric (GDP pc).
Table 1 summarizes the results of multivariate regressions by using ordinary least squares (OLS) models with
year-fixed effects for the period 2010-2015. The dependent variable is ln( GDP pc) and the independent variables of
interest are ECI for columns (1)-(4) and Fitness for columns (5)-(8) of Table 1. We find that ECI is a positive and
significant indicator for the level of economic development , and it solely explains 49.33% of the variance in ln(GDP
pc) among provinces (see column (1) of Table 1). Also, Urbani zation shows positive and significant relationship with
9

Table 1: Results of the multivariate regressions for the lev el of economic development.
OLS model with dependent variable: ln(GDP pc)
ECI Fitness
(1) (2) (3) (4) (5) (6) (7) (8)
ECI/Fitness0.2736*** 0.1699*** 0.1039*** 0.1398*** 0.2746*** 0.1707 *** 0.1270*** 0.1445***
(0.0237) (0.0302) (0.0304) (0.0307) (0.0235) (0.0390) (0. 0297) (0.0298)
ln(Population)0.0148 0.0014
(0.0269) (0.0296)
Urbanization0.7314*** 0.6349***
(0.1386) (0.1767)
Schooling21.488*** 22.165***
(3.0816) (2.8787)
ln(Innovation)0.0458* 0.0306
(0.0185) (0.0192)
ln(Trade)0.1107*** 0.1101***
(0.0180) (0.0175)
Observations 186 186 186 186 186 186 186 186
Adjusted R20.4933 0.5584 0.6277 0.5794 0.4961 0.5302 0.6402 0.5852
RMSE 0.3174 0.2963 0.2720 0.2891 0.3165 0.3056 0.2674 0.287 1
Notes : These multivariate regressions use the ordinary least squ ares (OLS) models to regress the level of economic developme nt (GDP pc) against
Economic Complexity Index (ECI) in columns (1)-(4) and Fitn ess Index in columns (5)-(8). These regressions include yea r-fixed effects using
data in the 2010-2015 period. Regression coe fficients of variables with standard errors (in the correspond ing parentheses) are reported under
significant level * p<0.1, ** p<0.05, and *** p<0.01. Adjusted R2indicates how many data points fall within the line of the reg ression
equation, and RMSE stands for the root mean square error.
ln(GDP pc). The factor ln(Population) has positive correla tion with ln(GDP pc), but the result is not significant (see
column (2) of Table 1). These three factors can explain 55.84 % of the variance in ln(GDP pc).
Economic research has revealed the importance of education , which raises people’s knowledge, skills, productiv-
ity and creativity, as a crucial and fundamental factor in ec onomic development [60, 61, 62]. Here, we find that both
Schooling (the ratio of students in higher education in a pro vince) and Innovation (the number of domestic granted
patents) are positively and significantly correlated with l n(GDP pc), as shown in column (3) of Table 1. The explana-
tory power of ECI remains positive and significant after cont rolling the effects of Schooling and Innovation. The three
factors together explain up to 62.77% of the variance in ln(G DP pc). In column (4) of Table 1, we find the positive
and significant correlation between ln(GDP pc) and Trade (th e total value of imports and exports of foreign trade).
ECI and ln(Trade) can explain 57.94% of the variance in ln(GD P pc).
Columns (5)-(8) of Table 1 present regression results using Fitness, where we find Fitness alone has the close
explanatory power as ECI (see column (1) and column (5)). How ever, one should notice that Fitness and ECI are
distinguishable from each other, for example, their formul as have essential di fferences (see Eq. (4) and Eq. (6)), the
distributions of the values that they produce are di fferent (see bar plots in the upper-left of Figure 6), and the co rrelation
between their values is 0.872 instead of 1 (see scatter plot a nd correlation value in the upper-left of Figure 6). Indeed,
after controlling the e ffects of Population and Urbanization, the explanatory power of Fitness is slightly inferior to ECI,
as indicated by the smaller values of Adjusted- R2(see column (6) of Table 1). Also, Fitness becomes more power ful
than ECI, after controlling the e ffects of Schooling, Innovation and Trade (see columns (7) and (8) of Table 1).
Moreover, we notice that ln(Innovation) loses its explanat ory power for ln(GDP pc) in the Fitness regression, as
shown in column (7) of Table 1. In short, ECI and Fitness are co mparative with each other, and both of them are
robust in explaining regional economic development.
4. Conclusions and Discussion
In this paper, we studied China’s regional economic complex ity based on 25 years’ firm data covering 31 provinces
and 70 industries. First, we mapped the firm data to a “Provinc e-Industry” bipartite network, based on which we found
that provinces with a high level of economic diversity trend to have the comparative advantages in industries with a
low level of ubiquity. Then, we quantified the competitivene ss of provinces through the non-monetary Economic
Complexity Index (ECI) by defining a set of linear iterative e quations between provinces’ economic complexity and
10

industries’ ubiquity. We found that provinces located arou nd the coast have larger ECIs, and the overall time evolution
of provinces’ rankings by ECI are relatively stable and slow . Further, after linking ECI with the economic develop-
ment, as measured by GDP pc and the relative income at urban (R ICU) and rural areas (RICR), and the relative income
differences (RICD), we found that ECI is positively and significa ntly correlated with the level of economic develop-
ment while negatively correlated with income inequality, s uggesting that ECI has potential to be a good non-monetary
indicator for revealing the status of regional economic dev elopment.
Moreover, we compared di fferent measures of non-monetary economic complexity and div ersity themselves (ECI,
Fitness, Diversity and Entropy), and explored their relati onships with some traditional monetary macroeconomic in-
dicators (GDP pc, RICU, RICR and RICD). We found that both ECI and Fitness have higher and positive correlations
with the level of economic development, compared to Diversi ty and Entropy. Together, we found the relative income
in rural area (RICR) outperforms the relative income in urba n area (RICU) in correlating with the economic diversity
measures. Moreover, we showed that all the measures of econo mic diversity and economic development are nega-
tively and significantly correlated with the income inequal ity (RICD), suggesting that provinces with higher economic
diversity and relative income have less income inequality. Finally, we checked the robustness of the explanatory power
of ECI and Fitness for economic development using multivari ate regressions with controlling for the e ffects of some
socioeconomic factors like Population, Urbanization, Sch ooling, Innovation and Trade. Results suggest that both ECI
and Fitness are robust in correlating with regional economi c development. Even though the causal relation between
economic complexity and development cannot be established yet, our work still contributes to the literature on the
complexity of regional economic systems within a nation.
Nevertheless, our results are not beyond limitations on dat a and modeling. The firm data contain a tiny fraction
of all Chinese firms. In fact, some very successfully and repr esentative firms are not included in our analysis just
because they are not listed in the two major stock markets. Al so, our data are limited by the spatial resolution
because provinces of China are first-level administrative d ivisions with heterogeneous land area. Some provinces
have large area but small population like Inner Mongolia, wh ile some may be opposite like Jiangsu. Moreover, the
“Province-Industry” network is built by counting how many fi rms in one province that operate in an industry without
considering the revenues and sizes of firms. This may cause po tential biases, to some extent, towards small firms
since they have less economic capacity, yet small contribut ion to regional economy development. In addition, the
emergence of new industries is limited by whether they have t he comparative advantage, which is not intuitive than
by the absolute number of firms. Furthermore, our current ana lysis is unable to establish causal relation between
economic complexity and development, limiting prediction as correlation in this context. Besides, due to the lack
of officially reported panel data of Gini coe fficients for Chinese provinces, the relative income di fferences in urban
and rural areas in 2010 is used as an alternative in estimatin g income inequality [50], which limits the time evolution
analysis and the comparison with other literature that used Gini coefficients. These aforementioned limitations call for
improvements towards better understanding the status of re gional economic development of China during its period
of economic expansion.
How to better quantify economic complexity in both theoreti cal and empirical ways is still an open question, which
remains further investigation. For example, as pointed out by previous studies [20, 21, 39], the two main economic
complexity indicators sometimes don’t show consistency wi th each other in ranking countries based on world trade
data, and traditional regression analysis is not particula rly meaningful for addressing the economic complexity prob –
lem. However, due to the lack of ground truth and the dependen cy on dataset in empirical studies, arguments on which
indicator performs best and which branch of theories is the m ost suitable to address this problem will not see their
ends and now urge on quantitative evaluation methods [42]. N evertheless, in recent years this branch of economic
complexity studies have found widely applications in ranki ng countries, industries, institutions, occupations and p rod-
ucts [14, 19, 21], see for example the Observatory of Economi c Complexity (OEC) (http: //atlas.media.mit.edu), the
DataViva (http://www.dataviva.info), and the Growthcom (http: //www.growthcom.eu). Meanwhile, the widely appli-
cation at different scales challenges the practicability of these method s, for example, the consistency or inconsistency
of ECI and Fitness results at national level and regional lev el. Keeping these potential limitations and promising real
world applications in mind, we would leave seeking data cove ring more firms with higher spatial resolution, checking
the robustness of findings using alternative definitions of n ew industry presence, exploring new methods to evaluate
the performance of economic complexity indicators and prop osing novel economic complexity metrics at di fferent
scales as future works.
Indeed, the increasing complexity of economic systems and t he data revolution of the past decade urge us on
11

a paradigm change in a more complexity-oriented and data-or iented economic thinking [63, 64, 65]. For example,
mainstream approaches measure economic development and pr edict economic growth using the aggregated GDP
based on economic census, financial market, foreign investm ent, physical capital, and so on [66, 67, 68]. However,
computing monetary factors, for instance GDP, is usually a n on-trivial task due to their involvement with considerable
resources for a long period [3]. In recent years, as the avail ability of large-scale data [4, 6] and the development of
complexity [19, 69] and network science [70, 71, 72], new con ceptual frameworks have been developed to address
these issues in a more e fficient way with far less cost. For example, based on world trad e data, “Product Space”
was proposed which reveals the status of national economic d evelopment and explains why not all countries face the
same opportunities in future development [17], and non-mon etary economic complexity and fitness were introduced
which have potential to predict future growth [18]. Moreove r, online social networks [3, 16, 73], mobile phone
data [1, 11, 74], satellite imagery [12, 75], geo-tagged ima ges [13] and web queries [76, 77] have also been applied
to reveal economic status, infer economic development, for ecast unemployment, predict poverty, map inequality,
quantify trading behavior [10] and correlate stock market m oves [78]. Although the new way of economic thinking is
not perfect [20, 21] and somehow limited by the availability of data and new statistical tools, there is a high possibilit y
that it will change the landscape of economic research in the near future [6].
Acknowledgments
The authors acknowledge the anonymous reviewers for critic al comments and constructive suggestions. The
authors thank Haixing Dai, Yiding Liu, Zhihai Rong, Qing Wan g, and Dan Yang for helpful discussions. This work
was partially supported by the National Natural Science Fou ndation of China (Grant Nos. 61433014 and 61673086).
Jian Gao acknowledges the China Scholarship Council for par tial financial support and the Collective Learning group
at the MIT Media Lab for hosting.
Appendix A.
Table A1: The two-digital abbreviations of province names i n China.
ID Abbreviation Province ID Abbreviation Province ID Abbreviation Province
1 BJ Beijing 12 AH Anhui 23 SC Sichuan
2 TJ Tianjin 13 FJ Fujian 24 GZ Guizhou
3 HE Hebei 14 JX Jiangxi 25 YN Yunnan
4 SX Shanxi 15 SD Shandong 26 XZ Tibet
5 NM Inner Mongolia 16 HA Henan 27 SN Shaanxi
6 LN Liaoning 17 HB Hubei 28 GS Gansu
7 JL Jilin 18 HN Hunan 29 QH Qinghai
8 HL Heilongjiang 19 GD Guangdong 30 NX Ningxia
9 SH Shanghai 20 GX Guangxi 31 XJ Xinjiang
10 JS Jiangsu 21 HI Hainan
11 ZJ Zhejiang 22 CQ Chongqing
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