How systemic imbalance shapes migration patterns

Article

How systemic imbalance shapes migration patterns: Evidence from China (1949–2012)

Chinese Sociological Dialogue 2017, Vol. 2(1-2) 3–17 ª The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/2397200917714593 journals.sagepub.com/home/csd

Peng Lu Central South University, Changsha, China

Abstract It has been found that migration flows follow the power-law distribution in terms of travel distances, and this work testifies that the distributions of origins and destinations fit the power-law as well, based on data collected during 1949–2012 in China. A social network model is conceptually built to measure each county’s out-degree (origins) and in-degree (destinations). It shows that both the distributions of origins and destinations follow the power-law distribution, and they are in the middle range of verified power-law exponents. With socio-economic implications, the power-law exponent measures the unbalance of resources and opportunities. Since the beginning of the reform and opening-up policy, China has experienced a transition from a redistributive economy to a market economy, i.e. from a centralized state to a decentralized state. The market or economy mechanism brings vast and in-depth development in various fields, and therefore continually reduces this inequality in mainland China. As long as the market plays the core role in the economy, exponents of origins and destinations will decline gradually, and they will both increase when the market is interrupted or weakened after the global financial crisis (2008–9). The distribution of resources and opportunities governs the migration flows. The market mechanism facilitates the balanced distribution of resources and opportunities, and therefore renders the more balanced trend of migration flows in China. Keywords China, migration pattern, power-law, systemic imbalance

Corresponding author: Peng Lu, Central South University, #932 Lushan South Road, Changsha 410083, China. Email: [email protected]

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Chinese Sociological Dialogue 2(1-2)

Introduction Migration is a basic activity of humans, and migration flows take place both in China and throughout the world (Abel & Sander, 2014; Shen, 2013). As the largest developing country, China has the biggest group of migrant workers in the world, numbering 70 million in 1993, 140 million in 2003, and 211 million in 2009 (Li, Wong & Hui, 2014). Most long-term migration flows are motivated mainly by the need for a livelihood, i.e. people migrate most often for better jobs (Jia & Tian, 2014). There are several theories that attempt to explain this. However, it seems that interactions between institutional and economic factors coincide in Chinese society (Shen, 2013; Lu & Wang, 2013), because the pivotal mechanism shaping migration patterns is the unequal distribution of resources and opportunities. This work aims to explore the pattern and verify the main agent of migration in China. In terms of migration patterns, it is believed that flows are not evenly balanced. It has been empirically demonstrated that the distribution of human mobility follows the power-law distribution (Gonzalez, Hidalgo, & Baraba´si, 2008; Yan, Han, Wang, & Zhou, 2013; Wang & Taylor, 2014) rather than random distribution (Gonzalez, Hidalgo, & Baraba´si, 2008). The power-law distribution is commonly applied to measure degrees of unequal distributions, such as earthquake scales (Gutenberg, 1944), citation times (Price, 1965), web visits (Adamic & Huberman, 2000), and scale-free networks (Baraba´si & Bonabeau, 2003). In terms of methods or tools, they utilize bank notes (Brockmann, Hufnagel, & Geisel, 2006), mobile phones (Gonzalez, Hidalgo, & Baraba´si, 2008), phone calls (Palchykov, Mitrovic, Jo, Saramaki, & Pan, 2014), and GPS information (Jiang, Yin, & Zhao, 2009) to record people’s locations and traces for certain time durations. However, there still exist some limitations, which will be the object of this study. First, durations previously were much shorter, numbered in months, weeks (Gonzalez, Hidalgo, & Baraba´si, 2008), or even days (Wang & Taylor, 2014). The initial question is: will this regularity hold for a longer history of people’s migration patterns? Using a much longer time span, from 1949 to 2012, our data record durations up to decades. Second, previous studies focused merely on travel distances (Gonzalez, Hidalgo, & Baraba´si, 2008; Yan, Han, Wang, & Zhou, 2013; Wang & Taylor, 2014), with limited attention paid to the network degree of locations. This work focuses on the power-law of degrees, including origins (out-degree) and destinations (in-degree). We explore the migration pattern over a number of decades and focus on the distribution of both in and outdegrees, which strengthens existing research. Besides addressing technical problems, the underlying factors shaping migration patterns as a socio-economic phenomenon will be explored. The concept of systemic imbalance is introduced to refer to the socio-economic factor of migration in China, which has not been adequately discussed before. As an important mechanism to shape migration, system imbalance refers to the uneven distributions of resources and opportunities. For historical reasons, resources are collinearly distributed in several major cities, areas or hubs. Therefore, the assumption is that people migrate for better resources and opportunities of improved livelihoods. In a certain period, if the distribution is uneven, the distribution of migration flows will be uneven as well, as long

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as this logic holds true. As the distribution becomes more balanced, then the distribution of flows would also be more balanced. Not aiming to solve theoretical debates, this work instead investigates the relationship between systemic imbalance and migration pattern.

Material and methods Data The data was collected from a national survey in 2012, with 12,696 residents interviewed to record their migration histories. The administrative structure of China consists of province, city and county, and the data is geographically based on the county level. The data of migration flows contains information about origins, destinations, and year for all the related counties in China. The data is constructed as a network, where each node represents a county and each flow is a directed relationship between them. For each node, both in-degree and out-degree are accumulatively calculated, in order to investigate whether degree distributions of nodes take on the power-law regularity.

Degrees The whole dataset is considered as a social network, R, where each node, i, represents one county, and each flow is deemed to be a directed relationship between two nodes, i and j (i 6¼ j). Each node is a six-digit number that is the administrative area code in 2010. Each node i has in-degrees, iin , and out-degrees, iout , summing up as the total degree in equation (1). The data is a set of three-dimensional vectors (O, D, t), where O refers to origin, D denotes destination, and t means the year when the move took place. For each year t that satisfies t 2 ½1949; 2012, we check the flows of that year t and calculate iin ðjtÞ and iout ðjtÞ, i.e. node i’s times of being origins and destinations. in i ðjtÞ ¼ count forigin ¼ ig ð1Þ iout ðjtÞ ¼ countfdestination ¼ ig The iin ðjtÞ and iout ðjtÞ are calculated as follows, if t is discrete, in equation (2) and (3).1 If t refers to the unit of year, then the in-degree is calculated as the summation of in-degree for each year between 1949 and 2012. Similarly, the out-degree is calculated as the summation of out-degree for each year between 1949 and 2012. 8 2012 X > > > > iin ðj1949 t 2012Þ ¼ > iin ðjtÞ > < t¼1949 ð2Þ 2012 X > > > out out > > i ðjtÞ i ðj1949 t 2012Þ ¼ > : t¼1949

For an arbitrary time interval of [tp , tq ], iin and iout are calculated as follows in equation (3).2 Terms tp and tq , which satisfy tp tq , refer to the same time unit, such as year, month, or week. As the time unit becomes smaller, then the in-degree and

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out-degree would be calculated as the continuous form for cases of days, minutes, seconds, milliseconds, and so on (see notes 1 and 2). 8 tq X > > > in > i ðjtp t tq Þ ¼ iin ðjtÞ > > < tp ð3Þ tq X > > > > iout ðjt t t Þ ¼ > iout ðjtÞ p q > : tp

Model The basic equation of power-law distribution is applied to test the distribution traits and measure the distribution of origins and destinations. In an arbitrary time interval, tp t tq , the out-degree is a series of numbers fiin g, where i stands for each node that has been the origin for at least one time, and iin represents each node i‘s times to be an origin. Then we tabulate these numbers in fiin g. The same operations can be done on fiout g for out-degrees. The power-law distribution usually takes on the form of y ¼ cxr , where x refers to the number of degrees, and y is the frequency or times of a certain degree level. For instance, x may mean degree of 1, and y refer to how many nodes or counties have a degree of 1. If the logarithm is taken at both sides of y ¼ cxr , we obtain equation (4), representing a straight line with logðcÞ as the intercept and r as the slope. The term C substitutes logðcÞ as the intercept in equation (4) that is used for least-square evaluation (OLS). logðyÞ ¼ logðcÞ r logðxÞ

ð4Þ

logðyÞ ¼ C r logðxÞ

ð5Þ

The negative of slope, r that satisfies r 0, refers to the power-law exponent, which indicates the inequality of distribution of in-degree and out-degree. If r ¼ 0, each degree gets the same frequency and the distribution is absolutely even or balanced. The larger r is, the more unequal the distribution will be. Here the power-law exponent r refers to imbalance scales of distributions of origins and destinations. If the exponent is larger, then the distribution of origins or destinations is more uneven, and it is more likely that several hubs, e.g. Beijing, Shanghai, and Canton, with the most resources and opportunities will emerge. Likewise, if there are fewer hubs then the distributions of destinations and origins will be more balanced with a lower power-law exponent r.

Logic of China’s migration The basic logic China’s migration is greatly affected by both economic and political factors (Yu & Zhang, 1998; Liang & White, 2011). Political factors govern and regulate the distribution of resources and opportunities, which ultimately shapes the pattern of migration.

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The political factors refer to national strategies, societal planning, and political movements, such as the hukou system (Chen, 2011; Shen, 2013), the Cultural Revolution (Yu & Zhang, 1998), etc. The economic factors put emphases on the livelihood demands of people, job opportunities, career mobility and so forth; the economic factors affect spontaneous traits, as people move to pursue better livelihoods (Chen, 2011; Jiang & Shi, 2015; Zhang & Song, 2003). However, the political factors such as planning, policies, and regulations are a prerequisite of socio-economic development in China (Shen, 2013). The revision or adjustment of political factors, such as related policies and regulations, causes changes in terms of distribution of resources and opportunities. As people in China move mainly to access better resources and richer opportunities of attaining them, the migration pattern varies accordingly across provinces of China. Therefore, the basic logic of China’s migration is that both policies and regulations determine the distribution of resources and opportunities, which ultimately shapes the pattern of migration. However, the pivotal agent shaping the pattern of China’s migration is the political factor. Planning, policies and regulations from the central government largely determine the distribution of resources and opportunities (Chen, 2011; Shen, 2013). Under strict policies and regulations, resources and opportunities are impartially distributed, so people flow to several major hubs with rich political, economic and cultural resources and opportunities. With looser restrictions and regulations, the distribution of resources and opportunities gets more and more balanced or diversified, with more and more developing cities or areas.

Policies and regulations among periods Historically, political factors such as policies and regulations have taken on different features and forms. The whole history is cut into four periods, each based on its features and forms: (a) the earlier stage (1949–1980). Migration flows in China are influenced by political factors, such as hukou policy (Xu & Palmer, 2011; Chen, 2011; Shen, 2013), political movements (like the Cultural Revolution), and policy guidance and national planning (Whyte & Parish, 1984; Liang & White, 1996). Migration was strictly regulated by governments before 1980. (b) the reform-and-opening-up stage (1980–2000). Under Deng Xiaoping’s leadership, China experienced a vast and in-depth transformation from a centralized economy to a free market. With looser political restrictions and more diversified resources and opportunities, people flowed to firms, corporations, and construction sites, boosting the economy yearly. (c) the new-century period (2000–12). Increasing numbers of people have become involved in the economy and migration process. In general, policies and regulations were increasingly tightened before 1980. After 1980 there were fewer restrictions on migration, and it was even encouraged by the governments of origins and welcomed by the governments of destinations. (d) the post-financial-crisis period (2009–12). After the global financial crisis in 2008, the migration trend waned. In the new century, China’s economy has been more and more closely embedded in the world economy (trade of commodities and services). Thus

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Figure 1. Migration flows of China (1949–2012). Each flow from an origin to a destination is plotted in Figure 1 as a tiny white line, and each white node represents a county. It indicates clearly that eastern and coastal areas have more flows than western provinces, and there exist several hot areas or hubs.

we see this fourth period as a double-edged sword, with the strong embeddedness in the global economy hurting the domestic economy. China has been substantially affected by the financial crisis in 2008, which ultimately changed the pattern of migration flows, especially for flows in the labor market. Therefore, this period tests how the migration pattern varies before and after the global financial crisis.

Systemic imbalance of resources and policies As an important mechanism to shape migration, system imbalance refers to the uneven distributions of resources and opportunities. Resources include political resources (policy and regulations), economic resources (commercial demand and opportunities) and cultural resources (education, history, entertainment, and work), while opportunities refer to the probabilities of accessing and utilizing these resources. For historical reasons, three types of resources are collinearly distributed in several major cities or areas (hubs). For instance, Beijing, Shanghai, and Canton are all centers of economy, culture, and entertainment, which reinforce their attractiveness. Quantifying and visualizing international migration flows between 1990 and 2010 has been impressively done by Abel and Sander (2014). The systemic imbalance can be visualized in Figure 1, which illustrates the pattern of China’s migration from 1949 to 2012. Although most areas are involved in the migration process, the inequality of the distribution of flows is explicit. There exist several hubs, such as Beijing, Shanghai, and Canton, and most flows take place at several hot areas, while other areas have few flows.

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Figure 2. Logic of China’s migration.

Beijing is the political, cultural, and educational center of China; Shanghai is the economic center of China and the center of the Yangtze River Delta as well; Canton is the center of the Pearl River Delta and also the economic center of South China. These hubs have rich political, economic, and cultural resources and opportunities, while most other cities have fewer. This phenomenon is described as the systemic imbalance.

Strong and weak logics Figure 2 presents the strong logic and weak logic of China’s migration. The strong logic is represented as a solid line, and it means that the adjustment of policies and regulations changes the distribution of resources and regulations, which ultimately shapes the migration pattern. The dashed linkage refers to the weak logic, which counteracts the strong logic and means that the distribution of migration may vary the distribution of resources and opportunities, and ultimately causes the revisions and adjustments of government policies and regulations. The data is used to test the existence of the weak and strong logics in China. In China the economy is under the heavy influence of political power, so the strong logic is obvious while the weak logic is latent. If the strong logic stands, it should be supported by the real data that the distribution of destinations or origins coincides with that of resources and opportunities. Hence, the power-law distribution is applied to test this regularity, because the power-law coefficient measures the inequality of distribution. This distribution provides a possible path to calculate and predict the distribution of migrants within areas and cities. And providing suitable public services fitting the dynamic distribution of migration would be promising, which is valuable for both cities of destinations and originals.

Results The power-law distribution of origins and destinations Distributions of origins (from) and destinations (to) are visualized separately in Figure 3, where this inequality is more apparent. The data of flows can be perceived as a social network. The number of the origin or the destination is deemed as the out-degree or in-degree of each county. Both distributions are unbalanced, as too many counties have fewer degrees. For origins, more flows start at the coastal and middle areas (Sichuan,

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Figure 3. Degree distributions of origins and destinations (1949–2012). The left half indicates the distribution of origins where a flow begins, and the right half shows the distribution of destinations that a flow points to. It can be seen that the distribution of origins is more diverse or balanced than that of destinations. Two plots below provide both these distributions.

Chongqing, Hunan, Hubei, Jiangxi, Anhui and Henan); for destinations, more flows point at major metropolises and other developed areas, such as Beijing, Shanghai, Jiangsu, Zhejiang, Fujian and Canton. The common dense areas fall into four hubs or urban belts, i.e. Bohai Economic Rim, Yangtze River Delta, Pearl River Delta, and South-East coastal areas. Figure 4 indicates that the overall exponent of origins rfrom that equals 1.67 and 1.07 for destinations rto . The former is higher than the latter, which means that the distribution of origins is more unbalanced than the destinations. As people in our data migrate mainly for career, school, or livelihood (Shen, 2013; Jia & Tian, 2014), they leave their towns of origin because of lack of resources, such as job opportunities. Hence, a higher rfrom implies that the inequality of resources distribution is relatively severe. Too many areas have too few resources while too few hubs own too many resources. The leakage of labor leads to further unfair distributions of human resources. Some provinces, such as Henan, Anhui, Sichuan, Chongqing, Guizhou, Hunan, Hubei, and Jiangxi, send huge numbers of laborers to other developed provinces and therefore fall behind socio-economically.

Historical trends This power-law of origins (from) and destinations (to) is also investigated under four periods (Table 1). For each period, the power law fits well, as the adjusted R2 is above

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Figure 4. Power-law exponents of origins and destinations (1949–2012). The two exponents are evaluated by OLS regression. For the left half, the exponent of origins’ distribution rfrom is 1.67+0.085 (0.0.85 as the standard error), and the adjusted R2 is 0.9016. For the right half, the exponent of destinations’ distribution rto is 1.076+0.09 (0.09 as the standard error), and the adjusted R2 is 0.7141.

80% and close to 100%. This means that both distributions follow the power-law regularity. Moreover, the unbalanced degree of origins is larger than that of destinations. From 1949 to 1980, rfrom (2.13) is larger than rto (1.64). Then, rfrom rfrom (2.13) is still higher than rto (1.64) from 1980 to 2000; during the new century, rfrom (1.80) is still bigger than rto (1.64). Hence, the destinations are more evenly distributed than the origins. Although the overall level is 1.67, rfrom varies, depending on different periods. During 1949–80, rfrom rfrom is 2.12 and 1.92 within 1980 to 2000, which suggests that the unfairness of resource distribution was serious or dangerous. Then, the opening up and reforming policy reduced the severity of this problem, as the decline of rfrom indicates. During the new century (2000–12), rfrom declines further from 1.92 to 1.80. With the increasing development, some firms and corporations expand their business into inner China, not merely coastal areas and several hubs. This consequently reduces longdistance migration and mitigates this situation. The distribution of resources is getting more and more balanced for long-lasting development. The global financial crisis in 2008 plays a negative role. China’s economy bears a huge recession pressure and labor flow is severely affected. As is shown in Figure 5, rfrom grows from 1.80 to 2.15 from 2009 to 2012. For the distribution of destinations, the overall exponent rto equals 1.07. It measures the imbalance of developments. As individuals flow to attractive places that are more advanced or developed, rto measures the imbalance of domestic development. Likewise, rto varies with historical periods. During the earlier stage, it equals 1.64 and declines to 1.55 during 1980 to 2000, which means that the imbalance of development was reduced after Deng Xiaoping’s reform and opening-up policy after 1979. Apart from coastal areas, the inner provinces experienced substantial developments of urbanization with cheaper land and labor, which made inner areas, such as Wuhan, Chongqing, and

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rto

rfrom

1980–2000 rto

rfrom

2000–2012 rto

rfrom

2009–2012 rto

C 5.23*** (0.3169) 4.49*** (0.2850) 5.98*** (0.2560) 5.26*** (0.2299) 6.27*** (0.3166) 4.57*** (0.2379) 5.88*** (0.3068) 3.98*** (0.2827) r 2.13*** (0.1661) 1.64*** (0.1325) 1.92*** (0.1072) 1.55*** (0.0885) 1.80*** (0.1162) 1.17*** (0.0737) 2.15*** (0.1431) 1.20*** (0.1053) Adj. R2 0.9314 0.9053 0.9412 0.9213 0.8922 0.8422 0.9337 0.8175

rfrom

1949–1980

Table 1. OLS regression outcomes of four periods. For each period, rfrom and rto and the constant term C are evaluated and listed in Table 1. The powerlaw model fits the data very well, as the adjusted R2 is close to 100%, e.g. 93% and 90% (1949–80), 94% and 92% (1980–2000), and 89% and 84% (2000–2012). The numbers in brackets are the standard errors.

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Figure 5. The evolution of rfrom and rto . (A) Four subfigures. From 1949 to 1980, the origins’ distribution is more unbalanced. After the reform toward the market economy, rfrom increases and it continues to increase from 1980 to 2012. The market is interrupted by the financial crisis during 2008 and 2009; rfrom therefore goes up because the distribution of resources becomes centralized again; (B) Four subfigures. From 1949 to 1980, the destinations’ distribution is more unbalanced. Since Deng Xiaoping’s reform toward the market economy, rto increases and it continues to increase between 1980 and 2012. The market is interrupted by the financial crisis (2008–9). Therefore rto goes up because the development difference between areas is sharpened.

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Table 2. History of the strong logic of migration in China.

1949–1980 1980–2000 2000–2012 2009–2012

Policies & Regulations

Resources & Opportunities

Migration Patterns

Power-Law Exponents

Controlled Released Released Setback & adjust

Centralized Balanced More balanced Less balanced

Centralized Diverse More diverse Less diverse

High Declines Declines more Rises slightly

Changsha, more attractive to migrant workers. This pattern of development reduces the imbalance situation and rto declines further from 1.55 to 1.17 during 2000 to 2012.

Conclusions and discussions In conclusion, migration flows follow the unique regularity of power-law distribution, with its exponent in the middle range. Figure 4 shows that the exponents of origins and destinations are 1.67 and 1.07. This is close to previous work about human migration patterns (Pickard, Pan, Rahwan, Cebrian, Crane, Madan, & Pentland, 2011), which indicates that the power-law exponent of travel distance is about 1.2. If we compare migration flows with other verified power-law distributions, such as 1.0 for website visits or English words, 2.0 for size of lunar craters, and 2.1 for sizes of planetary crusts, the exponent of migration flows is within the normal range. The power-law exponent measures and indicates the imbalance degree of distributions. As time goes by, it declines gradually under the influence of the market transition. As is indicated in Table 2, there exist strong positive correlations between the features of policies and regulations and the distribution of resources and opportunities: (1) During 1949 to 1980, government at all levels, especially the central government, controlled the allocation of resources and opportunities across China. The core feature for that period is that the political factor controls everything, so the distribution is highly centralized. (2) During 1980 to 2000, with the beginning of in-depth development of Deng’s reforms, the political system released some freedom to the distribution of market elements. Therefore, the distribution of resources and opportunities became more balanced. (3) During 2000 to 2012, the power system continued to release and transfer more space to the market. Meanwhile, the economy was strengthening yearly. With more than a decade of development since 2000, the distribution of resources and opportunities is becoming more and more balanced. The pattern of migration is directly determined by the distribution of resources and opportunities in China, the world’s largest developing economy, which has been reflected by the power-law exponents of both rfrom and rto . In the first phase (1949–80), the distribution of migration flows was highly centralized, with the highest power-law exponents of rfrom and rto ; in the second period, the distribution became diverse, as the distribution of resources and opportunities became more balanced. As a result, both rfrom and rto declined from 1980 to 2000; then, in the new century (2000–12), with the continuous development of the economy, the pattern of migration became increasingly diverse in that more and more cities were developing themselves and beginning to own

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more resources and provide more opportunities. Therefore, both rfrom and rto continued to decline from 2000 to 2012. However, it is still not adequate to declare that the distribution of resources and opportunities determines the pattern of migration flows and therefore validates the power-law exponent, as there might be other factors that play this role that have not been identified yet. Fortunately, the data about the global financial crisis provides the possibility to verify this assumption. After the outbreak of the global financial crisis in 2008, all the global giant economies, including China’s, were greatly hurt or undermined. Money disappeared, many firms closed, lots of construction projects ceased, and many unemployed workers migrated. State and city governments had to adjust their policies and regulations to cope with this urgent situation. The distribution of resources and opportunities became centralized or less balanced again, in that many young big cities shrank while traditional big cities were able to overcome difficulties brought on by the crisis. Greatly shaped by this situation, the migration pattern is getting more centralized or less diverse, which can be indicated by the fact that both rfrom and rto decline from 2009 to 2012. Therefore, it has been verified in Table 2 that the distribution of resources and opportunities determines or shapes the pattern of migration flows in China. The underlying mechanism or reason for this is the process of market transition that has taken place in China since 1980. The market transition promotes socio-economic developments and renders resources and opportunities more evenly distributed. Therefore the power-law exponent is reduced. Deng Xiaoping’s reform and opening-up policy brings out vast economic development and societal transformation, making distribution of resources or opportunities more balanced. In the earlier stage, China was a redistributive or centralized economy (Polanyi, 1957; Zhou, 1997), where resources such as opportunities and products were governed and allocated by the central government. Since 1980, under Deng Xiaoping’s leadership, China has begun its market transition from a redistributive economy towards a freer market (Xu & Palmer, 2011; Zhou, 1997; Nee, 1989). Resources no longer existed only in a few hubs – Beijing, Shanghai, and so on – while more and more areas were free to allocate their resources, leading to a more balanced distribution of opportunities. Therefore, more and more people, mainly migrant workers, moved domestically, chasing opportunities for better livelihoods (Jia & Tian, 2014). Due to the development of the market, more and more cities became attractive, making human flows less and less centralized (Nee, 1996). This is why the exponents declined from 1949 to 2012. Moreover, when the market mechanism was weakened in 2008–9 because of the global financial crisis, the flows became centralized again, therefore the exponents of in-degree and out-degree increased from 2009 to 2012. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding This work is supported by the National Natural Science Foundation of China (Grant No. 71673159), Beijing Natural Science Foundation (Grant No. 9164029), Beijing Social Science

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Foundation (Grant No. 16SRB014), and China Postdoctoral Science Foundation (Grant No. 2015M581122).

Notes 1. The iin and iout are calculated as follows if t is continuous

8 2012 Z > > > > > > > iin ðj1949 t 2012Þ ¼ iin ðjtÞ > > > < 1949

2012 Z > > > > > > > iout ðj1949 t 2012Þ ¼ iout ðjtÞ > > > : 1949

2. And iin and iout are calculated as follows if t is the continuous time interval.

8 Ztq > > > > > > iin ðjtp t tq Þ ¼ iin ðjtÞ > > > > < tp

> > > > > > > iout ðjtp t tq Þ ¼ > > > :

Zt

q

iout ðjtÞ tp

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Author biography Peng Lu is the Professor of Sociology in Central South University. Peng Lu obtains his Bachelor’s degree of Social Security at the China Youth University for Political Sciences (CYU) during 2004 and 2008. He gets the master’s degree of sociology at the Central Party School of China (CCPS) during 2008 and 2011, and the PhD of sociology in Tsinghua University during 2011 and 2014. From 2014 to 2016, he worked at Tsinghua University as a Post-doc in Department of Automation.